Difference between 'Quantum theories'

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Hey there

This may sound a bit silly to a lot of 'experts' but, what are the differences between standard qunatum mechanics, quantum field theory, and quantum electrodynamics?

Are they all predicting different aspects of natures workings, or has one superseded another? I get confused because I think standard qm has been done away with, and quantum field theory is what is used now. Perhaps a MAJOR correction is in order? :P
 

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  • #2
Pengwuino
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They're different fields, but none of them really supersede each other, they just are different areas of mechanics at the quantum level. Standard quantum mechanics is kind of like your newtonian mechanics of classical mechanics. QED is the electrodynamics of the classical world and field theory, I suppose is the field theory of the classical world heh. Not that that helps I suppose...
 
  • #3
Avodyne
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Quantum electrodynamics is a particular example of a quantum field theory.

A quantum field theory is a system whose basic objects are fields, and which is "quantized" by following a standard (or "canonical", which means "according to the laws of the church") procedure for turning a classical system into a quantum one.

I'm not sure what you mean by "standard" quantum mechanics. If you mean wave functions for nonrelativistic particles, this can be understood as a low-energy limit of an appropriate quantum field theory.
 
  • #4
alxm
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Yeah, I'm not sure what you would call 'standard quantum mechanics'.

The "original" quantum mechanics would basically be the Schrödinger equation. Now, the S.E. has several deficiencies: It doesn't take into account Special Relativity and it doesn't describe fields. Which doesn't mean you can't take fields into account in the S.E., just that they're classical fields and it doesn't describe the field itself. You can't really say the Schrödinger equation has been 'superseded' with respect to these things, though. The fact that it didn't describe these things was clear from the start. In fact, Einstein himself was there to point out the S.E. didn't obey relativity at the famous 1927 Solvay Conference. The work on remedying this had already started then, notably by another attendee, the young Paul Dirac.

So, in addition to the original quantum mechanics, you have relativistic quantum theory, which takes S.R. into account, and quantum field theory, which deals with fields quantum-mechanically. QED deals specifically with electromagnetic fields. QFT is usually relativistic, but for completeness I guess one should mention the existence of non-relativistic QFT, which sees some use in condensed-matter physics. There's a difference in formalism here; The "original" QM deals mainly with the wave function, whereas QFT/QED use http://en.wikipedia.org/wiki/Propagator" [Broken] (or Green's functions, in non-relativistic contexts). But you don't need quantized fields and special relativity to describe a lot of things. I'd even dare say that that most things of immediate practical significance don't, since almost all of chemistry and solid-state physics and material science ends up in that category. So the original quantum mechanics with its formalism is quite alive and well.

In my field (quantum chemistry) we don't need quantized fields, and despite some valiant efforts to introduce them (Hello Yngve..), propagator methods don't see much use. We have no need for QED in most cases, because those effects are too small to be relevant. Relativistic effects are relevant in heavy atoms (e.g. causing gold to be yellow and mercury to be a liquid). That gets handled either by applying a pseudopotential to the Schrödinger equation, mimicking the approximate effects, or by using the Dirac equation, which in this context can be viewed as a relativistic version of the Schrödinger equation.

But when the Dirac equation is used in QC, it's to get a relativistic description of the electrons, whereas the field only gets a semi-classical description (the "Coulomb gauge", where the magnetic potential is quantized but the Coulomb interaction isn't). This as opposed to the "Lorenz gauge", which leads to QED. So you use a theory where where it makes sense to do so, rather than what theory is 'best'. There's no point in complicating your description for an insignificant or nonexistent improvement in the result. Also, just because the Schrödinger equation has been around the longest, doesn't mean the formalism and methodology hasn't developed. Newtonian mechanics got reformulated in Lagrangian and Hamiltonian mechanics. The electronic Schrödinger equation has been reformulated in Density Functional Theory, for instance. (Which can be sub-divided further into the Kohn-Sham DFT and 'orbital-free' DFT, and again into chemical methods versus solid-state methods)
 
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  • #5
A. Neumaier
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what are the differences between standard quantum mechanics, quantum field theory, and quantum electrodynamics?
Quantum mechanics is the theory of that part of physics that can be understood in terms of linear operators on a Hilbert space called observables.

Quantum field theory is the theory of that part of quantum mechanics in which some observables depend on a space-time point. Quantum field theory is the least understood part of quantum mechanics.

Quantum electrodynamics is the quantum field theory in which the basic observables are the electromagnetic field and the electron current. Quantum electrodynamics is the best understood quantum field theory.
 
  • #6
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We have no need for QED in most cases, because those effects are too small to be relevant.
QED is essential for predicting reactions in laser chemistry.
 
  • #7
alxm
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QED is essential for predicting reactions in laser chemistry.
Could you elaborate on that and give an example, please?

QED is necessary for describing some absorption/emission processes (or all of them, if you want enough detail). That's not the same thing as predicting a (photo-)chemical reaction, which is something that starts after the absorption.

There wasn't much QED in the one grad course I took in laser chemistry.
 
  • #8
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Yeah, I'm not sure what you would call 'standard quantum mechanics'.

The "original" quantum mechanics would basically be the Schrödinger equation.
SE (schrödinger equation) can be linear (Standard Quantum Mechanics) or nonlinear (Non Standard Quantum Mechanics)
 
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  • #9
cgk
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QED is essential for predicting reactions in laser chemistry.
I'm also working in quantum chemistry, and I don't think I've ever seen QED corrections being applied to anything. Admittedly, I rarely read papers on <= 4electron systems where one can still make variational explicitly correlated wave functions, and where one could potentially obtain enough accuracy in the description of the electronic wave functions such that QED corrections might become relevant.

For systems with more electrons (say, up to 10--20), an accuracy of energy differences of about 1 meV or 0.1 kJ/mol is about the maximum one could expect to obtain with the currently available technology. And even that only in favorable circumstances and by combining everything in programs and methodology there currently is. Something like that is very not fun.
 
  • #10
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Could you elaborate on that and give an example, please?

QED is necessary for describing some absorption/emission processes (or all of them, if you want enough detail). That's not the same thing as predicting a (photo-)chemical reaction, which is something that starts after the absorption.
Enter the following keywords into http://scholar.google.com/ to get lots of references:
laser chemistry QED.

There is also a book called Molecular Quantum Electrodynamics, which describes QED for chemical applications.
 
  • #11
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Quantum mechanics is the theory of that part of physics that can be understood in terms of linear operators on a Hilbert space called observables.

Quantum field theory is the theory of that part of quantum mechanics in which some observables depend on a space-time point. Quantum field theory is the least understood part of quantum mechanics.

Quantum electrodynamics is the quantum field theory in which the basic observables are the electromagnetic field and the electron current. Quantum electrodynamics is the best understood quantum field theory.
I would like to suggest slightly different definitions.

The main feature of quantum field theory is that it describes systems where the number of particles can vary. So, it would be appropriate to say "quantum mechanics of systems with varying numbers of particles" instead of "quantum field theory". Otherwise, QFT is not different from *ordinary* quantum mechanics (which usually deals with systems having fixed number of particles). All the usual machinery of quantum mechanics (Hilbert spaces, wave functions, Hermitian operators, etc.) works in QFT just as well as in ordinary quantum
mechanics.

The interesting point is that once we have allowed the number of particles to change in QFT, there is no place to stop. We are forced to treat simultaneously all systems, where this number can be anywhere between zero and infinity, as well as superpositions of such states. Then the Hilbert space of QFT takes the specific form known as the Fock space, where the number of particles is a variable. Defining an interacting relativistic quantum theory in the Fock space is a challenging task. It appears that the easiest way to achieve this goal is to introduce certain abstract operator functions (called quantum fields) in the Fock space and build interaction operators (e.g., in the Hamiltonian) as polynomials of such operator functions. Hence the name "quantum field theory" for this approach. The most coherent explanation of this logic can be found in Weinberg's "The quantum theory of fields" vol. 1.

QED is a specific version of QFT applied to electromagnetic interactions of charged particles and photons.

Eugene.
 
  • #12
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The main feature of quantum field theory is that it describes systems where the number of particles can vary.
This is one feature but not the main one. The main feature, as the name says, is that it describes systems containing fields. For example, QED features operator-valued versions of the Maxwell equations for the electromagnetic field.

So, it would be appropriate to say "quantum mechanics of systems with varying numbers of particles" instead of "quantum field theory". Otherwise, QFT is not different from *ordinary* quantum mechanics
QFT is different from QM in the same sense as quantum physics is different from physics.
In both cases, the former is a proper subset of the latter.
 
  • #13
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This is one feature but not the main one. The main feature, as the name says, is that it describes systems containing fields. For example, QED features operator-valued versions of the Maxwell equations for the electromagnetic field.
Here we disagree. In my opinion fields (both Dirac field for electrons and Maxwell field for photons) are just mathematical tools for describing systems with variable number of particles. E.g., photons can be absorbed and emitted. Fields are not measurable by themselves.


QFT is different from QM in the same sense as quantum physics is different from physics.
In both cases, the former is a proper subset of the latter.
I basically agree with this. Though some people prefer the following terminology:

quantum theory = the most general quantum framework
quantum mechanics = quantum theory applied to systems with fixed number of particles
quantum field theory = quantum theory applied to systems with variable number of particles

Eugene.
 
  • #14
Fra
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I basically agree with this. Though some people prefer the following terminology:

quantum theory = the most general quantum framework
quantum mechanics = quantum theory applied to systems with fixed number of particles
quantum field theory = quantum theory applied to systems with variable number of particles
Good point.

With "basic quantum mechanics" I mean the abstractions of QM, state spaces, state spaces, expectations, measurements. Ie. the CORE feature of the measurement theory as it stands.

Wether it's fixed particle count, variable or field are all details within the process of indexing information. This is IMHO partly an open question, and I am not satisfied with the mainstream ways, RG etc. For ME at least, analysing this problem unavoidably connects to the problem of understanding the emergence of the spacetime index, which necessarily also connets to some aspects of gravity. I also think this couples back to the basic QM structure, which needs to be revised or put in a larger context (generalized).

In my opinion fields (both Dirac field for electrons and Maxwell field for photons) are just mathematical tools for describing systems with variable number of particles. E.g., photons can be absorbed and emitted. Fields are not measurable by themselves.
I think that not only fields, but also the notion of particles are all just different ways to index and structure information. Actually the INDEX itself, does carry information in the sense that you can apply the ergodic principle to any index and get an a priori expectation. My opinon is that the exact way of indexing information is something that's not yet understood.

What I consider to elementary (measurable as you say) are simply a set of distinguishable events. I make not interpretation that these corrsepond to "particle counts" at a detector. I just see them as distinguished events. This is the a discrete structure, where the "field" picture is more like an smooth approximation.

To think of "particles" is far too confusing and even more classical. I just think of the "directly observable" as detector counts, sitting in the observers boundary (loosely speaking). The internal structure is then recoded forms of histories of counts, and in this recoding - there is a preferred index. I think changing the index amounts to different forms of datacompression. This is how I picture the selection principle.

/Fredrik
 
  • #15
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Here we disagree. In my opinion fields (both Dirac field for electrons and Maxwell field for photons) are just mathematical tools for describing systems with variable number of particles. E.g., photons can be absorbed and emitted. Fields are not measurable by themselves.
Of course, fields require detectors to be measurable. But the electromagnetic field is not only the photons - these are only the harmonic excitations of the latter.


some people prefer the following terminology:

quantum theory = the most general quantum framework
quantum mechanics = quantum theory applied to systems with fixed number of particles
quantum field theory = quantum theory applied to systems with variable number of particles
Only a few people like you. Most quantum physicists know why quantum field theory is called quantum _field_ theory.

Even Weinberg, your favorite textbook writer, writes (on p. xii):
''The point of view of this book is that quantum field theory [...] is the only way to reconcile the principles of quantum mechanics [...] with those of relativity.''
This view is incompatible with your above definitions of quantum mechanics and quantum field theory.
 
  • #16
cgk
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Enter the following keywords into http://scholar.google.com/ to get lots of references:
laser chemistry QED.
I've looked through the first 10 pages of that, and I found no title indicating any relation to chemical reactions. In fact, most of them don't even deal with molecules.

There is also a book called Molecular Quantum Electrodynamics, which describes QED for chemical applications.
According to the amazon description, this also doesn't deal with reactions.
 
  • #17
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I've looked through the first 10 pages of that, and I found no title indicating any relation to chemical reactions. In fact, most of them don't even deal with molecules.

According to the amazon description, this also doesn't deal with reactions.
Indeed, I had somehow mixed up molecular spectroscopy with laser chemistry.
''this self-contained, systematic introduction features formal derivations of the quantized field matrix elements for numerous laser-molecule interaction effects: one- and two-photon absorption and emission, Rayleigh and Raman scattering, linear and nonlinear optical processes, the Lamb shift, and much more.''
https://www.amazon.com/dp/0121950808/?tag=pfamazon01-20

http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/43521/1/JChemPhys_115_3497.pdf
treats chemical reactions on a QED basis, but I must admit, this is one of very few papers.
 
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  • #18
alxm
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[link]treats chemical reactions on a QED basis, but I must admit, this is one of very few papers.
Even that paper isn't actually treating the reaction using QED; they're treating the reaction using HF/6-311G* (which has an error many orders of magnitude greater than any pure QED effects). They're doing a QED calculation on the results of those calculations to get a spatial decomposition of the electronic energy, something which the authors think gives a more interesting qualitative picture of what's going on during the reaction. There are other, more common, ways of doing that. Frontier-orbital analysis, Bader analysis, a whole bunch of ways that utilize the electrostatic potential, etc.

Using QED to calculate properties which you can use to visualize aspects of a reaction is of course not the same thing as saying a QED treatment is necessary to describe the reaction itself. As cgk said, the maximum accuracy of QC methods is about 0.1 kJ/mol, and purely QED effects are several orders of magnitude smaller than that. Yet, about 1 kJ/mol is about what's considered "chemical accuracy". I just don't see how a purely-QED effect could be energetically large enough to "make-or-break" a chemical reaction at just about any temperature.
 
  • #19
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As cgk said, the maximum accuracy of QC methods is about 0.1 kJ/mol, and purely QED effects are several orders of magnitude smaller than that. Yet, about 1 kJ/mol is about what's considered "chemical accuracy". I just don't see how a purely-QED effect could be energetically large enough to "make-or-break" a chemical reaction at just about any temperature.
I now realize where my misunderstanding came from.

QED is needed to model the interaction between a laser and a molecule, since this involves both photons and electrons. Thus it is needed to derive from first principles
the conditions under which a laser is able to excite a molecule from its ground state to an excited state - where it moves on a different potential energy surface, which may enables reaction that are otherwise impossible or inefficient.

However, concerning the practice of laser chemistry, one can forget QED once one has
drawn the qualitative conclusion from QED that adding laser light of the right frequency to bridge the energy gap between ground state and excited state has the desired effect.
And one doesn't need QED at all if one simply assumes this statement without invoking QED, but referring instead to experimental practice.
 
  • #20
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.
Even Weinberg, your favorite textbook writer, writes (on p. xii):
''The point of view of this book is that quantum field theory [...] is the only way to reconcile the principles of quantum mechanics [...] with those of relativity.''
This view is incompatible with your above definitions of quantum mechanics and quantum field theory.
Weinberg's book is remarkably different from other QFT textbook. Weinberg *does not* start his book like "Here we have this thing called field. Let us apply quantum mechanics to it and see what we get."

Instead, his starting point is: "We have things called particles. We want to calculate their relativistically invariant scattering amplitudes. How can we build the appropriate Hamiltonian?"

Eugene.
 
  • #21
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Weinberg's book is remarkably different from other QFT textbook. Weinberg *does not* start his book like "Here we have this thing called field. Let us apply quantum mechanics to it and see what we get."

Instead, his starting point is: "We have things called particles. We want to calculate their relativistically invariant scattering amplitudes. How can we build the appropriate Hamiltonian?"
Instead of quoting fictitious lines put into the mouth of Weinberg, you'd read what he actually writes in his preface! His starting point is (quoted verbatim with some omissions indicated explicitly):

''Why another book on quantum field theory? [...] specific examples are frequently used [...] chosen from contemporary particle physics or nuclear physics as well as from quantum electrodynamics. [...] The point of view of this book is that quantum field theory is the way it is because (aside from theories like string theory that have an infinite number of particle types) it is the only way to reconcile the principles of quantum mechanics [...] with those of relativity.''

This quote contains all (two) occurrences of the word ''particle'' in the first five paragraphs, while the word ''field'' appears quite frequently, and my previous quote is there, too.

In the sixth paragraph come his reasons why particles enter the picture: ''The most immediate and certain consequences of relativity and quantum mechanics are the properties of particle states, so here particles come first - they are introduced in Chapter 2''

Indeed, Chapter 1 is exclusively about classical field equations. Particles make their appearance first on p.67 bottom. At this point, the book is already more than 10% on the way. In sharp contrast to your claim, the particles do not appear as starting point but (as promised in the preface) as the most immediate and certain consequences of relativity and quantum mechanics.

From Chapter 4 on he discusses (in the remaining 72% of the book) the less immediate consequences of relativity and quantum mechanics - called quantum field theory.
 
  • #22
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Arnold,

it seems that we are reading the same book, but understand it quite differently. Let me recap briefly what I've learnt from Weinberg.

Chapter 1: I skip this as it is just an historical introduction.

Chapter 2: Definition of particles as unitary irreducible representations of the Poincare group. No mention of fields.

Chapter 3: Definition of the S-matrix as transition amplitudes between different *particle* states. Requirement of the relativistic invariance of the S-matrix. The important piece is eqs. (3.5.11) - (3.5.18), which suggest that the theory can be made relativistically invariant if the interaction Hamiltonian is represented as an integral of some "density" with a particular transformation law and commutators. Note also that there is no proof that this is the *only* way to build relativistic interactions. Note the phrase "let's try the hypothesis" before (3.5.11). No mention of fields.

Chapter 4. The cluster decomposition principle. Creation and annihilation operators of *particles* are introduced. The important point is that the theory can be made cluster-separable if the Hamiltonian is expressed as a polynomial in c/a operators (4.4.1) with smooth coefficient functions. No mention of fields.

Chapter 5. Here Weinberg tries to build specific examples of Hamiltonians with properties specified in Chapter 3. This is where the fields finally come into play. Weinberg defines free fields as some abstract linear combinations of creation and annihilation operators with postulated properties, like the covariant transformation law (5.1.6) - (5.1.7) and (anti)commutators (5.1.32). He briefly mentions field equations (5.1.34) and then says "...we start with the particles, and derive the fields according to the dictates of Lorentz invariance, with the field equations arising almost accidentally as a byproduct of this construction."

It seems pretty clear to me that Weinberg is not interested in fields by themselves, and he does not assign any physical significance to fields. For him, the only reason to introduce free quantum fields is to have a mathematical tool for constructing relativistically invariant and cluster separable interaction Hamiltonians. Once such an interaction is constructed and expressed in terms of *particle* creation and annihilation operators, we can happily forget about fields. We will have all rules (see Chapter 6) for calculating scattering amplitudes for any configuration of initial *particles*, and this is the only thing we really care about in quantum field theory. *Particle* scattering cross-sections and energies of *particle* bound states are the only numbers that can be reliably calculated in QFT and compared with experiment. Fields play a certain role at intermediate steps of these calculations, but this role is completely technical.

Possibly one can pretend that field is some kind of material substance and try to use QFT to calculate the field strength at given points. But is this information useful? Is there an experiment to verify these numbers? I don't think so. Even the most revered *electromagnetic field* is an approximate concept. As far as I know, light is not a continuous field or wave. If we make light of sufficiently low intensity and look at it with sufficiently high resolution, we will find out that it consists of indivisible and countable particles called photons. So, actually, there are no truly continuous material fields or waves in nature. Everything becomes granular and particle-like if we look at it with a high enough resolution.

Eugene.
 
  • #23
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it seems that we are reading the same book, but understand it quite differently.
Yes indeed.

It seems pretty clear to me that Weinberg is not interested in fields by themselves, and he does not assign any physical significance to fields.
You completely ignore what Weinberg himself writes as motivation and goal in his preface, and replace it by your subjective conjectures about the interests of Weinberg, though these contradict his statements in the preface.

Once such an interaction is constructed and expressed in terms of *particle* creation and annihilation operators, we can happily forget about fields. We will have all rules (see Chapter 6) for calculating scattering amplitudes for any configuration of initial *particles*, and this is the only thing we really care about in quantum field theory.
Weinberg never forgets the fields. All later chapters are full of them.

*Particle* scattering cross-sections and energies of *particle* bound states are the only numbers that can be reliably calculated in QFT and compared with experiment.
You don't realize how much is done with quantum field theory. People calculate a lot more: Thermodynamic properties of equilibrium states, hydrodynamic equations for flowing fields, kinetic transport equations governing the behavior of semiconductors, etc.. The fact that this is not in Weinberg's book doesn't mean that it is not done. If scattering of particles were the only application of QFT, the latter wouldn't play the fundamental role it plays.

Possibly one can pretend that field is some kind of material substance and try to use QFT to calculate the field strength at given points. But is this information useful? Is there an experiment to verify these numbers?
Every engineer is able to measure the electromagnetic field at a particular point.

Even the most revered *electromagnetic field* is an approximate concept.
Everything in physics is an approximate concept when applied to reality.

In particular, the particle concept is even more approximate than the field concept, since matter frequently behaves far from particle-like.
 
  • #24
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Weinberg never forgets the fields. All later chapters are full of them.
I agree that fields make a useful mathematical concept. They allow to simplify calculations considerably. For example, it would be very difficult (though possible) to calculate loop integrals without using fields and propagators but relying only on interaction expressed as a function of creation/annihilation operators. The mathematical usefulness of fields does not prove that quantum field is a measurable physical concept.


You don't realize how much is done with quantum field theory. People calculate a lot more: Thermodynamic properties of equilibrium states, hydrodynamic equations for flowing fields, kinetic transport equations governing the behavior of semiconductors, etc..
I am not an expert in this, but I always thought that the current in semiconductors can be reliably calculated with usual classical methods. Actually, presently I am working in semiconductor industry where such calculations are performed routinely without any involvement of quantum mechanics or QFT. I can agree that simple quantum effects (e.g., tunneling) may become visible in nanostructures at low temperatures. However, I've never heard that radiative corrections (whose description demands QFT methods) have any visible effect on the behavior of semiconductors. It is very difficult to see such corrections (e.g., the Lamb shift) in super precise measurements of individual atoms. But observation of radiative corrections in such a mess as a working semiconductor device would be truly amazing. So, I remain sceptical.

It would be a different matter if you are talking about condensed matter quantum field theory, which uses approximately continuous fields (such as the phonon field or electron current density). I agree that this heuristic quantum field theory has made a lot of progress in such areas as superconductivity, etc. But I thought that we are discussing fundamental, presumably exact relativistic QFT of elementary particles, which is the subject of Weinberg's book.


If scattering of particles were the only application of QFT, the latter wouldn't play the fundamental role it plays.
I am glad that we agree about that.


Every engineer is able to measure the electromagnetic field at a particular point.
... by placing a test charged *particle* at that point and measuring its acceleration.



In particular, the particle concept is even more approximate than the field concept, since matter frequently behaves far from particle-like.
Like when?

Eugene.
 
  • #25
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I agree that fields make a useful mathematical concept.
But Weinberg wrote a book about physics. Clearly he thinks that fields make a useful physical concept.

The mathematical usefulness of fields does not prove that quantum field is a measurable physical concept.
The expectation values of the quantum electromagnetic field is routinely measured by many engineers, hence the quantum electromagnetic field is as much a measurable physical concept as the position of a particle, where one commonly - namely except in diffraction experiments - also measures only the expectation value.



I am not an expert in this, but I always thought that the current in semiconductors can be reliably calculated with usual classical methods. Actually, presently I am working in semiconductor industry where such calculations are performed routinely without any involvement of quantum mechanics or QFT.
One doesn't need quantum methods on the engineering level, just as one doesn't need quantum theory to use superconducting solenoids as magnets.

Nevertheless, the classical formulas are all derived from quantum field theory.
The behavior of semiconductors on the atomic level is determined in solid state physics by QED in an external periodic potential with or without impurities. In some cases, nonrelativistic QED (or even coarser approximations) is enough, but not always: http://scholar.google.com lists about 18,800 references for the keywords
semiconductor relativistic

The valence electrons in a metal are so much delocalized that the electrons must be regarded as a quantum fluid (described by a electron density field) rather than as a collection of particles. Moreover, even when talking in the 'particle language, solid state physicists think of the valence electrons as quasi-particles whose very definition is in terms of fields.


I can agree that simple quantum effects (e.g., tunneling) may become visible in nanostructures at low temperatures. However, I've never heard that radiative corrections (whose description demands QFT methods) have any visible effect on the behavior of semiconductors.
The classical Maxwell equations don't fall from heaven as classical equations independent of quantum mechanics but are the macroscopic limit of QED. This is completely independent of either semiconductors or radiative corrections.


It would be a different matter if you are talking about condensed matter quantum field theory, which uses approximately continuous fields (such as the phonon field or electron current density). I agree that this heuristic quantum field theory has made a lot of progress in such areas as superconductivity, etc. But I thought that we are discussing fundamental, presumably exact relativistic QFT of elementary particles, which is the subject of Weinberg's book.
The _only_ difference between condensed matter quantum fields and relativistic quantum fields is that the former have nonlocal interactions and transform under the Galilei group, while the latter have local interactions and transform under the Poincare group. But both are based on the same concept of a quantum field.

Quantum fields are also more basic than particles in condensed matter theory. Indeed, the concept of identical particles has no logical basis on the particle level and must be introduced in an ad hoc way to get agreement with experiment. And it completely destroys the very basis of a reasonable particle concept: the possibility to assign observables (self-adjoint operators) to the position of a particle inside a multiparticle system. There _are_ no such observables.

On the other hand, identical particles are one of the most elementary consequences of the
quantum field concept, and certain smeared fields are both observable in the formal sense of being self-adjoint operators on the Hilbert space of the system _and_ in the sense of measurable expectation values.




Like when?.
Electrons bound in a molecule or a crystal. Chemists think of them in terms of charge density (a field concept), and solid state physicists think of them in terms of a fluid (another field concept). Particles are not experimentally identifiable except under very extreme circumstances.


Finally, the difficulties you have in forcing QED into the Procrustes bed of a pure particle picture
are proof of that the latter is unnatural and incomplete. Indeed, the canonical Fock space electrons that figure in your approach lack the electromagnetic field with which they need to be accompanied as asymptotic, physical particles) in order to exhibit the correct infrared behavior.
You would notice further problems if you were to extend your theory to handle the relaticistic plasma (see, e.g., H.A. Weldon, Phys. Rev. D 26, 1394–1407 (1982), http://llacolen.ciencias.uchile.cl/~vmunoz/download/papers/w82.pdf [Broken] ). I wonder how you'd do that in your version of QED.

By the way, in your book you give a fairly complete list of publications related to Faddeev's dressing method, which is the basis of your perturbative particle-only approach to QED. Maybe you want to add the following one....

I.Ya. Aref'eva
Renormalized scattering theory for the Lee model
Teoret. Mat. Fiz. 12 (1972) 331-348
Theor. Math. Phys. 12 (1972), 859-872
http://mi.mathnet.ru/eng/tmf2995

Maybe you should send a link to your book to your fellow countryman Faddeev, whom you owe so much, and ask him why he gave up his dressing approach in favor of the usual field theoretic methods that lead him to the today accepted solution of the infrared problem in QED.
 
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