I Confusion about Scattering in Quantum Electrodynamics

[Demystifier]

How do we know this. This interacting vacuum Ω is nothing like the free vacuum and is a complicated object from what I hear so how do you know the Particle Density n(r,t) or the Energy density is 0.

The interacting vacuum is complicated when expressed in terms of eigenstates of the free Hamiltonian. But it is simple when expressed in terms of eigenstates of the interacting Hamiltonian. In the latter sense, it has zero particles and lowest possible energy.

 

[physwiz222]

The interacting vacuum is complicated when expressed in terms of eigenstates of the free Hamiltonian. But it is simple when expressed in terms of eigenstates of the interacting Hamiltonian. In the latter sense, it has zero particles and lowest possible energy.

Still wont the Interacting Vacuum have a nonzero Particle Number Density or Energy Density

 

[Demystifier]

Still wont the Interacting Vacuum have a nonzero Particle Number Density or Energy Density

How do you define interacting vacuum? How do you define particle number density?

 

[A. Neumaier]

Still wont the Interacting Vacuum have a nonzero Particle Number Density or Energy Density

No. Vacuum means ''nothing'', even in QFT!

 

[Morbert]

In quantum chemistry, if you expand the ground state of the interacting Hamiltonian in an energy eigenbasis of a mean-field approximation, some elements of that basis corresponding to excited states will have nonzero amplitudes. (A method called Configuration Interaction)

Is it similar here? If you expand the ground state of the interacting Hamiltonian in the eigenbasis of the free Hamiltonian, will you get some elements of the basis corresponding to > 0 particles having nonzero amplitudes?

 

[A. Neumaier]

In quantum chemistry, if you expand the ground state of the interacting Hamiltonian in an energy eigenbasis of a mean-field approximation, some elements of that basis corresponding to excited states will have nonzero amplitudes. (A method called Configuration Interaction)

Is it similar here? If you expand the ground state of the interacting Hamiltonian in the eigenbasis of the free Hamiltonian, will you get some elements of the basis corresponding to > 0 particles having nonzero amplitudes?

In an interaction relativistic QFT there is no particle number operator, hence no sensible notion of particle number, so the question does not make sense. Moreover, you cannot expand the interacting theory in terms of the free Hamiltonian since they act on disjoint Hilbert spaces.

Only little is left from the particle picture: For theories without massless fields, there are discrete mass shells defining a notion of bound states. But everything with mass $\ge$ twice the minimal mass is in the continuous spectrum of the mass, and can be resolved into particles only asymptotically (for infinite time). For theories like QED with massless fields, the mass spectrum is only continuous and the particle notion is even questionable at infinity.

 

[physwiz222]

In an interaction relativistic QFT there is no particle number operator, hence no sensible notion of particle number, so the question does not make sense. Moreover, you cannot expand the interacting theory in terms of the free Hamiltonian since they act on disjoint Hilbert spaces.

Only little is left from the particle picture: For theories without massless fields, there are discrete mass shells defining a notion of bound states. But everything with mass $\ge$ twice the minimal mass is in the continuous spectrum of the mass, and can be resolved into particles only asymptotically (for infinite time). For theories like QED with massless fields, the mass spectrum is only continuous and the particle notion is even questionable at infinity.

Is there a density operator of some kind for interacting fields where one can talk about the field’s density like is there an equivalent of the electron number density for an interacting field.

 

[A. Neumaier]

Is there a density operator of some kind for interacting fields where one can talk about the field’s density like is there an equivalent of the electron number density for an interacting field.

In QED one has the mass density and the charge density, both scalar-valued, and the vector-valued energy-momentum density. All vanish by definition in the physical vacuum state (what you called the interacting vacuum).

 

[PeterDonis]

Moderator's note: Some posts on a changed topic have been spun off to a separate thread:

https://www.physicsforums.com/threa...tween-quantum-and-classical-behavior.1055703/

 

[physwiz222]

This naive approach was tried very early in the history of QFT and discarded since it led to UV divergences; see, e.g., Wikipedia.

Haag's theorem showed rigorously that this naive approach cannot work, i.e., why renormalization is unavoidable if one starts with Fock space.

If this is so then why is it in Many Body Theory for solids as an example that Green’s Functions and Correlation functions can be computed at finite times as well as perturbative methods for finite time dynamics unlike particle physics if Haag’s Theorem is such a big issue. Is Haag’s theorem only an issue in Relativistic QFT and not in nonrelativistic many body theory. Do Green’s Functions somehow circumvent this restriction that the interacting states cant be expressed as fock states.

 

[A. Neumaier]

If this is so then why is it in Many Body Theory for solids as an example that Green’s Functions and Correlation functions can be computed at finite times as well as perturbative methods for finite time dynamics unlike particle physics if Haag’s Theorem is such a big issue.

Because this is nonrelativistic quantum physics. There the hard problems of QFT are absent. Haag's theorem assumes local quantum physics in Minkowski spacetime.

Is Haag’s theorem only an issue in Relativistic QFT and not in nonrelativistic many body theory.

Yes.

Do Green’s Functions somehow circumvent this restriction that the interacting states cant be expressed as fock states.

Not if constructed in the usual Fock-based way.

 

[physwiz222]

Because this is nonrelativistic quantum physics. There the hard problems of QFT are absent. Haag's theorem assumes local quantum physics in Minkowski spacetime.

Yes.

Not if constructed in the usual Fock-based way.

I do wonder with all this in mind why no textbooks ever bring these issues up with describing finite time dynamics of even simple scattering processes as this seems to be a very open unsolved problem. It seems that the very notion of particles in Interacting QFT is dubious at best and the idea of finite time dynamics even for scattering is inherently Nonperturbative no matter how weak the coupling constant is as Haag’s Theorem essentially invalidates using perturbation theory in the same way as regular QM. I wonder why no books ever bring up these major issues as they seem to be open problems. Also why are people talking about Quantum Gravity and Supersymmetric 10 dimensional Branes when we don't even have a proper coherent theory and understanding of basic interacting Relativistic QFT and can only map between states in the far past and future even for weak couplings forget Bound states.

 

[weirdoguy]

as this seems to be a very open unsolved problem.

Most textbooks don't delve into open unsolved problems, mainly because they are unsolved and open

Also why are people talking about Quantum Gravity and Supersymmetric 10 dimensional Branes when we don't even have a proper coherent theory and understanding of basic interacting Relativistic QFT

So everyone should halt their work until people from QFT community solve their problems? One can work on quantum gravity or branes without using interacting QFT, so there is no issue there. And maybe work on those models will shed some light on Haag.

 

[A. Neumaier]

I do wonder with all this in mind why no textbooks ever bring these issues up with describing finite time dynamics of even simple scattering processes as this seems to be a very open unsolved problem.

The reason is that textbooks are usually not about open problems but about the basic understanding that works.

It seems that the very notion of particles in Interacting QFT is dubious

Only at finite times.

Nonperturbative no matter how weak the coupling constant is as Haag’s Theorem essentially invalidates using perturbation theory in the same way as regular QM.

But it does not invalidate renormalized perturbation theory, which is what the textbooks teach.

why are people talking about Quantum Gravity and Supersymmetric 10 dimensional Branes when we don't even have a proper coherent theory and understanding of basic interacting Relativistic QFT

Because it is easier to write papers related to theoretical proposals that cannot be tested than to solve problems open for more than 60 years, where the best minds have tried and not succeeded.

 

[physwiz222]

Most textbooks don't delve into open unsolved problems, mainly because they are unsolved and open
So everyone should halt their work until people from QFT community solve their problems? One can work on quantum gravity or branes without using interacting QFT, so there is no issue there. And maybe work on those models will shed some light on Haag.

The statement was more hyperbolic the point is that its weird that we are trying to seek a theory of Quantum Gravity but we dont even have a proper solidly built Relativistic Quantum theory for the EM field. It was more of saying its frustrating when people say we are so close to a theory of everything but gravity just wont cooperate when this isnt the case. In reality we are a long ways off as we struggle and stumble to find a solidly built description of the other forces.

 

[physwiz222]

The reason is that textbooks are usually not about open problems but about the basic understanding that works.

Only at finite times.

But it does not invalidate renormalized perturbation theory, which is what the textbooks teach.

Because it is easier to write papers related to theoretical proposals that cannot be tested than to solve problems open for more than 60 yeatrs, where the best minds have tried and not succeeded.

Renormalized Perturbation Theory is only a way to get rid of infinities for asymptotic scattering. It cant describe finite time dynamics. At finite times Relativistic QFT is from what I know inherently nonperturbative no matter the coupling due to Haag’s Theorem. When I say the notion of Particles in interacting QFT is Dubious at best I mean at finite times I should have mentioned.

Anyway its really frustrating to hear scientists and popsci act as if we are so close to a theory of everything but gravity just wont cooperate. In reality we are nowhere near we cant even develop a coherent solidly build description of the Quantum EM field all we can do is map in and out states not the finite time dynamics. Interacting QFT is very very very very poorly understood. The very notion of a particle and perturbation theory at finite times is dubious at best.

 

[physwiz222]

The reason is that textbooks are usually not about open problems but about the basic understanding that works.

Only at finite times.

But it does not invalidate renormalized perturbation theory, which is what the textbooks teach.

Because it is easier to write papers related to theoretical proposals that cannot be tested than to solve problems open for more than 60 yeatrs, where the best minds have tried and not succeeded.

Also the thing is I am not saying books should go in depth with Algebraic QFT just mentioning why we have to limit to asymptotic times because the notion of Perturbation Theory and Particles at finite times is invalid due to Haag’s Theorem. Just maybe a sentence justifying the need for asymptotic times.

 

[A. Neumaier]

Renormalized Perturbation Theory is only a way to get rid of infinities for asymptotic scattering. It cant describe finite time dynamics.

It can't describe the finite-time dynamics of a finite number of particles, since the particle concept fails at finite times. But it can describe the finite-time dynamics of fields in important sectors, for example those related to hydrodynamics. See the reference to Calzetta and Hu given earlier, which you seem to have ignored.

The very notion of a particle and perturbation theory at finite times is dubious at best.

It does not and cannot exist. There is no particle number operator in interacting QFTs. Only fields make sense at finite times.

 

[vanhees71]

The primary observables in QFT are defined by some local operator-correlation functions. These are $N$-point functions, which in principle can be calculated for finite times for a given initial state (statistical operator) using the Schwinger-Keldysh real-time contour technique.

Of course, there's the usual trouble with the UV divergences when calculating these N-point functions, and to my knowledge there's not solution for this renormalization problem for such "off-equilibrium situations". You also have to use some resummation since in contradistinction to the special cases of vacuum QFT for calculating S-matrix elements for scattering processes or equilibrium QFT the strictly order-by-order in hbar or coupling constant expansion-parameter perturbation theory is not described by naive perturbation theory.

One approach is the Kadanoff-Baym $\Phi$-functional method, also known as the two-particle irreducible (2PI) formulation or the Cornwall-Jackiw-Tomboulis approach. There you derive self-consistent approximations for the one-body Green's function and the corresponding self-consistent self-energy, which is given by "skeleton diagrams" derived from the functional approach. Despite the notorious (and to my knowledge unsolved) renormalization problem there are a view studies solving the full Kadanoff-Baym equations for simple truncations and in lower space-time dimensions (to soften the renormalizability problem). One example is a study in simple $\phi^4$ theory in (1+2) dimensions

https://arxiv.org/abs/nucl-th/0401046
https://doi.org/10.1016/j.nuclphysa.2004.07.010

Usually the Kadanoff-Baym equations are used to derive quantum-transport equations, using additional approximations like the gradient expansion ("coarse graining"), leading to transport theories that work with some caveats even for broad resonances rather than "particles". It's further simplified if the spectral functions don't develop too large (collisional) widths. Then you can also apply the quasiparticle approximation, which leads to usual relativistic Boltzmann-Uehling-Uhlenbeck transport equations. For this there's a vast amount of literature related with the study of ultrarelativistic heavy-ion collisions. Some examples are

Y. B. Ivanov, J. Knoll, H. v. Hees and D. N. Voskresensky,
Soft Modes, Resonances and Quantum Transport, Phys.
Atom. Nucl. 64, 652 (2001),
https://arxiv.org/abs/nucl-th/0005075Y. B. Ivanov, J. Knoll and D. N. Voskresensky, Self-consistent
approximations to non-equilibrium many-body theory, Nucl.
Phys. A 657, 413 (1999),
https://arxiv.org/abs/hep-ph/9807351

Y. B. Ivanov, J. Knoll and D. Voskresensky, Resonance
transport and kinetic entropy, Nucl. Phys. A 672, 313 (2000),
https://doi.org/10.1016/S0375-9474(99)00559-X

Y. B. Ivanov, J. Knoll and D. N. Voskresensky, Resonance
Transport and Kinetic Entropy, Nucl. Phys. A 672, 313
(2000), https://arxiv.org/abs/nucl-th/9905028

Y. Ivanov, J. Knoll and D. Voskresensky, Selfconsistent
approach to off-shell transport, Phys. Atom. Nucl. 66, 1902
(2003), https://doi.org/10.1134/1.1619502

J. Knoll, Y. B. Ivanov and D. Voskresensky, Exact
Conservation Laws for the Gradient Expanded
Kadanoff-Baym Equations, Ann. Phys. (NY) 293, 126 (2001),
https://arxiv.org/abs/nucl-th/0102044

W. Cassing, From Kadanoff-Baym dynamics to off-shell
parton transport, Eur. Phys. J. ST 168, 3 (2009),
https://doi.org/10.1140/epjst/e2009-00959-x

and many more.

 

[physwiz222]

The primary observables in QFT are defined by some local operator-correlation functions. These are $N$-point functions, which in principle can be calculated for finite times for a given initial state (statistical operator) using the Schwinger-Keldysh real-time contour technique.

Of course, there's the usual trouble with the UV divergences when calculating these N-point functions, and to my knowledge there's not solution for this renormalization problem for such "off-equilibrium situations". You also have to use some resummation since in contradistinction to the special cases of vacuum QFT for calculating S-matrix elements for scattering processes or equilibrium QFT the strictly order-by-order in hbar or coupling constant expansion-parameter perturbation theory is not described by naive perturbation theory.

One approach is the Kadanoff-Baym $\Phi$-functional method, also known as the two-particle irreducible (2PI) formulation or the Cornwall-Jackiw-Tomboulis approach. There you derive self-consistent approximations for the one-body Green's function and the corresponding self-consistent self-energy, which is given by "skeleton diagrams" derived from the functional approach. Despite the notorious (and to my knowledge unsolved) renormalization problem there are a view studies solving the full Kadanoff-Baym equations for simple truncations and in lower space-time dimensions (to soften the renormalizability problem). One example is a study in simple $\phi^4$ theory in (1+2) dimensions

https://arxiv.org/abs/nucl-th/0401046
https://doi.org/10.1016/j.nuclphysa.2004.07.010

Usually the Kadanoff-Baym equations are used to derive quantum-transport equations, using additional approximations like the gradient expansion ("coarse graining"), leading to transport theories that work with some caveats even for broad resonances rather than "particles". It's further simplified if the spectral functions don't develop too large (collisional) widths. Then you can also apply the quasiparticle approximation, which leads to usual relativistic Boltzmann-Uehling-Uhlenbeck transport equations. For this there's a vast amount of literature related with the study of ultrarelativistic heavy-ion collisions. Some examples are

Y. B. Ivanov, J. Knoll, H. v. Hees and D. N. Voskresensky,
Soft Modes, Resonances and Quantum Transport, Phys.
Atom. Nucl. 64, 652 (2001),
https://arxiv.org/abs/nucl-th/0005075Y. B. Ivanov, J. Knoll and D. N. Voskresensky, Self-consistent
approximations to non-equilibrium many-body theory, Nucl.
Phys. A 657, 413 (1999),
https://arxiv.org/abs/hep-ph/9807351

Y. B. Ivanov, J. Knoll and D. Voskresensky, Resonance
transport and kinetic entropy, Nucl. Phys. A 672, 313 (2000),
https://doi.org/10.1016/S0375-9474(99)00559-X

Y. B. Ivanov, J. Knoll and D. N. Voskresensky, Resonance
Transport and Kinetic Entropy, Nucl. Phys. A 672, 313
(2000), https://arxiv.org/abs/nucl-th/9905028

Y. Ivanov, J. Knoll and D. Voskresensky, Selfconsistent
approach to off-shell transport, Phys. Atom. Nucl. 66, 1902
(2003), https://doi.org/10.1134/1.1619502

J. Knoll, Y. B. Ivanov and D. Voskresensky, Exact
Conservation Laws for the Gradient Expanded
Kadanoff-Baym Equations, Ann. Phys. (NY) 293, 126 (2001),
https://arxiv.org/abs/nucl-th/0102044

W. Cassing, From Kadanoff-Baym dynamics to off-shell
parton transport, Eur. Phys. J. ST 168, 3 (2009),
https://doi.org/10.1140/epjst/e2009-00959-x

and many more.

Interesting anyway which observables do the N Point Functions exactly allow u to compute and do they encode the finite time dynamics of all possible observables of the theory.

 

[physwiz222]

It can't describe the finite-time dynamics of a finite number of particles, since the particle concept fails at finite times. But it can describe the finite-time dynamics of fields in important sectors, for example those related to hydrodynamics. See the reference to Calzetta and Hu given earlier, which you seem to have ignored.It does not and cannot exist. There is no particle number operator in interacting QFTs. Only fields make sense at finite times.

I didnt ignore but these techniques in Nonequilibrium QFT are very different from “standard” perturbation theory for renormalizing scattering amplitudes. When I refer to renormalized Perturbation theory I am referring to standard QFT perturbation theory for S Matrix elements.

 

[vanhees71]

Interesting anyway which observables do the N Point Functions exactly allow u to compute and do they encode the finite time dynamics of all possible observables of the theory.

You can, in principle, describe observables like densities of charges, the energy-momentum tensor, etc. It's pretty much the quantum version of a continuum theory like hydrodynamics.

 

[A. Neumaier]

I didnt ignore but these techniques in Nonequilibrium QFT are very different from “standard” perturbation theory for renormalizing scattering amplitudes.

Only in computational details, but not in the basic goals (need to avoid infinities) and techniques (use of N-point functions).

When I refer to renormalized Perturbation theory

When I refer to renormalized perturbation theory I refer to what physicists themselves call renormalized perturbation theory. You'd do well to extend your horizon!

I am referring to standard QFT perturbation theory for S Matrix elements.

You cannot complain that there is no finite time version of that, since S-matrix elements are by definition asymptotic objects!

 

[physwiz222]

Only in computational details, but not in the basic goals (need to avoid infinities) and techniques (use of N-point functions).

When I refer to renormalized perturbation theory I refer to what physicists themselves call renormalized perturbation theory. You'd do well to extend your horizon!

You cannot complain that there is no finite time version of that, since S-matrix elements are by definition asymptotic objects!

Anyway I think if Mainstream Particle Physics is to progress and get out of the 50 year stagnation it should abandon or at least move attempt to move beyond the S matrix approach to mapping in and out states and asymptotic time calculations and focus on computing correlation functions at finite times to describe finite time dynamics of scattering and many other processes like cosmological phenomena. I think the field should address the foundational issues as well as find ways to address the implications of haag’s theorem.

The reason why innovation is so hard in the field is because most is just scattering amplitudes at infinite times so when all you have is a hammer everything looks like a nail. I think Particle Physics should take an approach similar to Many Body Theory for condensed matter. Theres a reason condensed matter is a popular thriving field while particle physics is stagnating. Also when I refer to Particle Physics I mean Mainstream High Energy Physics I know some people do other things that are non asymptotic but those are non mainstream. I know the difficulties of this new approach but it should be attempted this is what Particle Physics needs a focus on Finite time dynamics and Correlation Functions of Fields, not String Theory or Supersymmetry.

I think this instrumentalist approach of just predicting numbers in a collider is not a good way of doing physics. Even if the equations describe “what we can say about Nature” We should still try and understand how they describe systems, particles, and fields evolving dynamically even if limited. The main issue with an instrumentalist approach is why do we even make physics theories. We dont invent physics as fodder for experimentalists because they are bored. Also when we have confirmed our theories what next do we declare it useless. This is why I think an instrumentalist view in particle physics isnt a good approach. Who cares if our colliders cant probe those timescales our instruments also cant probe the evolution of the wavefunction in standard QM yet its important and computed and simulated. We also can't probe the inside of a black hole yet physicists are interested.

I know the mathematical difficulties associated with anything other than asymptotic states in High Energy QFT but more physicists should at least attempt it and give it a shot and focus on New Nonperturbative Methods and some new nontraditional perturbative methods as if we are to describe finite time dynamics we will likely have to move past or at least expand and modify perturbation theory as well as describe nonperturbative phenomena. I apologize if this is a lengthy essay.

 

[weirdoguy]

I think the field should address the foundational issues as well as find ways to address the implications of haag’s theorem.

Um, and why in the world you think it doesn't?

 

[vanhees71]

Anyway I think if Mainstream Particle Physics is to progress and get out of the 50 year stagnation it should abandon or at least move attempt to move beyond the S matrix approach to mapping in and out states and asymptotic time calculations and focus on computing correlation functions at finite times to describe finite time dynamics of scattering and many other processes like cosmological phenomena. I think the field should address the foundational issues as well as find ways to address the implications of haag’s theorem.

What do you mean by "stagnation"? If there's one field in contemporary theoretical physics it's the Standard Model of elementary particles based on relativistic QFT and the S-matrix.

What's often forgotten is that there are also successful applications of relativistic many-body QFT in the field of relativistic heavy-ion collisions, including the evaluation of the cross-over pseudo-critical temperature for the confinement-deconfinement/chiral cross-over transition at vanishing baryochemical potential with thermal lattice QCD, but also the derivation of (partially off-shell) quantum-transport equations as well as the derivation of various versions of viscous relativistic hydrodynamics from it.

Last but not least one must not forget the vast applications of relativstic QFT in quantum optics and AMO physics.

The reason why innovation is so hard in the field is because most is just scattering amplitudes at infinite times so when all you have is a hammer everything looks like a nail. I think Particle Physics should take an approach similar to Many Body Theory for condensed matter. Theres a reason condensed matter is a popular thriving field while particle physics is stagnating. Also when I refer to Particle Physics I mean Mainstream High Energy Physics I know some people do other things that are non asymptotic but those are non mainstream. I know the difficulties of this new approach but it should be attempted this is what Particle Physics needs a focus on Finite time dynamics and Correlation Functions of Fields, not String Theory or Supersymmetry.

As I said, that's precisely what's done. QFT is more a metatheory of almost all of physics rather than being limited to the single field of relativistic HEP physics, and there almost always all you need is the S-matrix approach (with the important exception of neutrino-oscillations, where you need to take into account the finite distance between source and detector making use of the wave-packet ansatz for asymptotic states).

I think this instrumentalist approach of just predicting numbers in a collider is not a good way of doing physics. Even if the equations describe “what we can say about Nature” We should still try and understand how they describe systems, particles, and fields evolving dynamically even if limited. The main issue with an instrumentalist approach is why do we even make physics theories. We dont invent physics as fodder for experimentalists because they are bored. Also when we have confirmed our theories what next do we declare it useless. This is why I think an instrumentalist view in particle physics isnt a good approach. Who cares if our colliders cant probe those timescales our instruments also cant probe the evolution of the wavefunction in standard QM yet its important and computed and simulated. We also can't probe the inside of a black hole yet physicists are interested.

The "instrumentalist approach" is all there is within objective natural sciences. You may speculate what's the philosophical meaning of the description in terms of QFT, it doesn't add anything to the fact that all we can objectively say about Nature is, how she behaves in a given situation. After all these are all mathematical models, no more no less.

I know the mathematical difficulties associated with anything other than asymptotic states in High Energy QFT but more physicists should at least attempt it and give it a shot and focus on New Nonperturbative Methods and some new nontraditional perturbative methods as if we are to describe finite time dynamics we will likely have to move past or at least expand and modify perturbation theory as well as describe nonperturbative phenomena. I apologize if this is a lengthy essay.

That's also what's done. 20 years ago the Kadanoff-Baym approach of real-time off-equilibrium many-body QFT became applied in the relativistic domain, leading to the above mentioned derivations of transport and hydrodynamic description. Somewhat later, given the difficuluties of this Phi-derivable 2PI approach with (gauge) symmetries also the 1PI (Dyson Schwinger) approach has been worked out in more detail, and is very successful in collaboration with lattice QFT. Last but not least in more recent years the functional renormalization group has become vigorously and still is applied in the field of relativsitic heavy-ion collisions.

There is indeed much more than the S-matrix approach in the application of relativistic QFT than you might be aware of!

 

[physwiz222]

What do you mean by "stagnation"? If there's one field in contemporary theoretical physics it's the Standard Model of elementary particles based on relativistic QFT and the S-matrix.

What's often forgotten is that there are also successful applications of relativistic many-body QFT in the field of relativistic heavy-ion collisions, including the evaluation of the cross-over pseudo-critical temperature for the confinement-deconfinement/chiral cross-over transition at vanishing baryochemical potential with thermal lattice QCD, but also the derivation of (partially off-shell) quantum-transport equations as well as the derivation of various versions of viscous relativistic hydrodynamics from it.

Last but not least one must not forget the vast applications of relativstic QFT in quantum optics and AMO physics.

As I said, that's precisely what's done. QFT is more a metatheory of almost all of physics rather than being limited to the single field of relativistic HEP physics, and there almost always all you need is the S-matrix approach (with the important exception of neutrino-oscillations, where you need to take into account the finite distance between source and detector making use of the wave-packet ansatz for asymptotic states).

The "instrumentalist approach" is all there is within objective natural sciences. You may speculate what's the philosophical meaning of the description in terms of QFT, it doesn't add anything to the fact that all we can objectively say about Nature is, how she behaves in a given situation. After all these are all mathematical models, no more no less.

That's also what's done. 20 years ago the Kadanoff-Baym approach of real-time off-equilibrium many-body QFT became applied in the relativistic domain, leading to the above mentioned derivations of transport and hydrodynamic description. Somewhat later, given the difficuluties of this Phi-derivable 2PI approach with (gauge) symmetries also the 1PI (Dyson Schwinger) approach has been worked out in more detail, and is very successful in collaboration with lattice QFT. Last but not least in more recent years the functional renormalization group has become vigorously and still is applied in the field of relativsitic heavy-ion collisions.

There is indeed much more than the S-matrix approach in the application of relativistic QFT than you might be aware of!

Interesting reply. just one thing when I say instrumentalist approach is an issue I dont mean philosophy of physics type things but rather that we should focus on how the system evolves according to the equations rather than just predicting some numbers and nothing more. I am not talking about this in the sense of philosophy of Physics but rather that things like how systems evolve and interact are important and the most important thing to use a theory for is conceptual understanding of the phenomena. Predictions are important dont get me wrong but the ultimate reason why we invent a theory is to understand nature in some way even if its limited. Just wanted to clarify what I meant by “instrumentalism is not the best way of doing physics”.

 

[physwiz222]

What do you mean by "stagnation"? If there's one field in contemporary theoretical physics it's the Standard Model of elementary particles based on relativistic QFT and the S-matrix.

What's often forgotten is that there are also successful applications of relativistic many-body QFT in the field of relativistic heavy-ion collisions, including the evaluation of the cross-over pseudo-critical temperature for the confinement-deconfinement/chiral cross-over transition at vanishing baryochemical potential with thermal lattice QCD, but also the derivation of (partially off-shell) quantum-transport equations as well as the derivation of various versions of viscous relativistic hydrodynamics from it.

Last but not least one must not forget the vast applications of relativstic QFT in quantum optics and AMO physics.

As I said, that's precisely what's done. QFT is more a metatheory of almost all of physics rather than being limited to the single field of relativistic HEP physics, and there almost always all you need is the S-matrix approach (with the important exception of neutrino-oscillations, where you need to take into account the finite distance between source and detector making use of the wave-packet ansatz for asymptotic states).

The "instrumentalist approach" is all there is within objective natural sciences. You may speculate what's the philosophical meaning of the description in terms of QFT, it doesn't add anything to the fact that all we can objectively say about Nature is, how she behaves in a given situation. After all these are all mathematical models, no more no less.

That's also what's done. 20 years ago the Kadanoff-Baym approach of real-time off-equilibrium many-body QFT became applied in the relativistic domain, leading to the above mentioned derivations of transport and hydrodynamic description. Somewhat later, given the difficuluties of this Phi-derivable 2PI approach with (gauge) symmetries also the 1PI (Dyson Schwinger) approach has been worked out in more detail, and is very successful in collaboration with lattice QFT. Last but not least in more recent years the functional renormalization group has become vigorously and still is applied in the field of relativsitic heavy-ion collisions.

There is indeed much more than the S-matrix approach in the application of relativistic QFT than you might be aware of!

By Stagnation I mean the 50 year period of stagnation in particle physics happening now. Also I know there are applications to QFT beyond high energy particle physics like relativistic hydrodynamics I mentioned this my criticism was the standard S Matrix approach of mainstream particle physics. Also I think this relativistic kinetic/hydrodynamic approach that you bring up is what particle physics needs not string theory and supersymmetry. I think it should be more mainstream. I am aware there is more than the s matrix but I argue it should be the norm not some niche thing.

You also say the S Matrix is all you need for HEP. Technically true but I disagree as it gives a limited view. It cant describe finite time dynamics which I think is important. Also I think this relativistic kinetic/hydrodynamic approach or similar methods is better for High energy particle interactions for finite time dynamics of observables like densities and correlation functions than the standard s matrix approach.

 

[physwiz222]

Um, and why in the world you think it doesn't?

Standard QFT in mainstream high energy physics high energy physics is based on computing scattering amplitudes at infinite time with the S Matrix. All it can really compute is mapping between input and output states. There are indeed other applications like relativistic kinetic theory which Vanhees mentions and I argue they should become mainstream. Particle physicists arent worried about foundational issues their goal is to predict asymptotic scattering to compare with collider results and dont forget string theorists in their la la land of 10 dimensional supersymmetric branes.

 

[vanhees71]

By Stagnation I mean the 50 year period of stagnation in particle physics happening now. Also I know there are applications to QFT beyond high energy particle physics like relativistic hydrodynamics I mentioned this my criticism was the standard S Matrix approach of mainstream particle physics. Also I think this relativistic kinetic/hydrodynamic approach that you bring up is what particle physics needs not string theory and supersymmetry. I think it should be more mainstream. I am aware there is more than the s matrix but I argue it should be the norm not some niche thing.

You also say the S Matrix is all you need for HEP. Technically true but I disagree as it gives a limited view. It cant describe finite time dynamics which I think is important. Also I think this relativistic kinetic/hydrodynamic approach or similar methods is better for High energy particle interactions for finite time dynamics of observables like densities and correlation functions than the standard s matrix approach.

There is no stagnation in HEP physics. One should realize that the finding that there's nothing beyond the standard model in the realm we observe with our current experiments is also progress. That's why the LHC including the existing detectors got recently upgraded and new detectors were built (already with the first direct measurement of collider-produced neutrinos). It may well be that after all something new is found with these new instruments.