Qft Definition and 956 Threads

I was reading Diagrammatica by Veltman and he treats the photon field as a massive vector boson in which gauge invariance is disappeared and the propagator has a different expression than in massless photon. After some googling, I found that this is one way to formulate QED which has the...

Does unitarity have to be obeyed in a full quantum gravity model?

This seems important to me, since in some interactions, particles are produced by pairs of opposite momentum in the rest frame of the interaction.

How do we map experimental measurements of quantum fields, such as those seen in accelerators, to the theory's mathematical formalism? When we see images of particle tracks produced in accelerators such as the LHC, I think it's safe to say a measurement (or series of measurements) has been...

Hi all, I'm interested in the interplay between condensed matter and high energy theory. I'm a bit more than half-way through peskin and schroeder (done with part II, RG and critical phenomena). What I find out is that I'm still sorely lacking in ability to read any of the current research in...

There is a draft of Srednicki's QFT book available for free online (here: https://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf). I have a book voucher and, since I couldn't find it in the library, was thinking of buying it so long as the content of the book was sufficiently better (i.e...

In This wikipedia article is said: "If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a...

In Coleman's QFT lectures, I'm confused by equation 7.57. To give the background, Coleman is trying to calculate the scattering matrix (S matrix) for a situation in which the Hamiltonian is given by $$H=H_{0}+f\left(t,T,\Delta\right)H_{I}\left(t\right)$$ where ##H_{0}## is the free Hamiltonian...

Bostelmann, H., Fewster, C. J., & Ruep, M. H. (2021). Impossible measurements require impossible apparatus. Physical Review D, 103(2), 025017.

While in QFT we remove infinite energy problem with renormalization procedure, asking e.g. "what is mean energy density in given distance from charged particle", electric filed alone would say $$\rho \propto |E|^2 \propto 1/r^4 $$ But such energy density would integrate to infinity due to...

I know that studying QFT requires understanding Lie Groups and infinitesimal generators as they correspond to symmetry transformations. I want to study or take a course (offered by my university) in QFT in the coming academic year and I have the option to take a abstract algebra course offered...

There are some articles from the 1980s where the authors discuss 1D quantum oscillators where ##V(x)## has higher than quadratic terms in it but an exact solution can still be found. One example is in this link: https://iopscience.iop.org/article/10.1088/0305-4470/14/9/001 Has anyone tried to...

I have been studying scattering process in QFT, but i am stuck now because i can't understand how this integral was evaluated: $$\int dp\space \frac{1}{\sqrt{p^2+c²}}\frac{1}{\sqrt{p^2+k²}}\space p² \space d\Omega \space \delta(E_{cm}-E_{1}-E_{2})$$$ Where Ecm = c + k, E1 is the factor in the...

While classical mechanics uses single action optimizing trajectory, QM can be formulated as Feynman ensemble of trajectories. As in derivation of Brownian motion, mathematically it is convenient to use nonphysical: nowhere differentiable trajectories - should it be so? Can this connection be...

For a real scalar field, I have the following expression for the field operator in momentum space. $$\tilde{\phi}(t,\vec{k})=\frac{1}{\sqrt{2\omega}}\left(a_{\vec{k}}e^{-i\omega t}+a^{\dagger}_{-\vec{k}}e^{i\omega t}\right)$$ Why is it that I can discard the phase factors to produce the time...

Given the commutation relation $$\left[\phi\left(t,\vec{x}\right),\pi\left(t,\vec{x}'\right)\right]=i\delta^{n-1}\left(\vec{x}-\vec{x}'\right)$$ and define the Fourier transform as...

I want to show that the action staying the same action after taking ##A^\mu \to A^\mu + \partial ^\mu \chi##, for the first term I suceeded in showing the invariance using the fact ##[\partial ^ \mu , \partial ^\nu]=0## but for the second term I'm getting: ##\epsilon^{\alpha\mu\nu}A_\alpha...

Summary:: I want to study QFT 1 in the upcoming semester, so what are the prerequisites to study it. By QFT 1 I mean Classical field theory, Canonical Quantization, Feynman Diagrams, and QED. I am trying to self study QM from Griffiths' Introduction to Quantum Mechanics book. What are the sub...

Hello, So I was reading about Hawking radiation and I read a QFT interpretation of it. It went something like this: A vacuum contains virtual particles (vacuum energy), which in qft can be described as waves that are out of phase and cancel each other out (matter and antimatter). I a black...

why in QFT 4-momentum is conserved? how can it be derived from basic principles of the Hamiltonian formalism? Is it conserved because of the golden rule?

Moderator's Note: Thread spun off from previous thread due to topic change. I see. Basically you are worried by stuff a mathematical physicist would study with fancy schmancy functional analysis. I'm not worried too much by such stuff because I don't think that actual infinities (actually...

I am reading the claymath problem here: http://claymath.org/sites/default/files/yangmills.pdf on page 6, in the comments (section 5), they call a local operator to be an operator that satisifies: ##\mathcal{O}(\vec{x})=e^{-i\vec{P}\cdot \vec{x}}\mathcal{O}e^{i\vec{P}\cdot \vec{x}}## where...

In Quantum Field Theory and the Standard Model by Schwartz, he defines the Hamiltonian for the free electromagnetic field as (page 20, here's a link to the book). This follows (in my understanding) from the fact that the amplitude of the field at a given point in space oscillates as a simple...

Hi! My name's Logan Knox and I'm aspiring to eventually understand the physics and nature of the quantum world in its totality, and I have a LONG way to go, but I have to get there by asking the right questions, and I think this is the first step to finding the right question to ask for this...

When we apply creation operator in vacuum we certainly have one particle,similarly for annihilation operator.Then what is stand for chance(probability) in QFT?

Hi there, In QFT, a free scalar field can be represented by the lagrangian density $$\mathcal{L} = \frac{1}{2}\left(\partial\phi\right)^2 - \frac{1}{2}m^2\phi^2$$ I would like to find a classical system that has the same lagrangian. If we consider the transversal motion of an elastic string...

\begin{align} \psi_L \rightarrow (1-i \vec{\theta} . \frac{{\vec\sigma}}{2} - \vec\beta . \frac{\vec\sigma}{2}) \psi_L \\ \psi_R \rightarrow (1-i \vec{\theta} . \frac{{\vec\sigma}}{2} + \vec\beta . \frac{\vec\sigma}{2}) \psi_R \end{align} I really cannot evaluate these from boost and rotation...

In quantum mechanics there is no operator for time (problem with unbounded energy). position is no more an operator in field theory. was there still a problem in QM?

Under the Schrodinger Picture, nonrelativistic Quantum Mechanics for a fixed number of particles is highly nonlocal, e.g. Quantum Entanglement. But Quantum Field Theory is local. Why is that? Is it because QFT was created to accommodate SR, which, as a classical theory, is local? As always...

I am trying to get a foothold on QFT using several books (Lancaster & Blundell, Klauber, Schwichtenberg, Jeevanjee), but sometimes have trouble seeing the forest for all the trees. My problem concerns the equation of QED in the form $$ \mathcal{L}_{Dirac+Proca+int} = \bar{\Psi} ( i \gamma_{\mu}...

Why can't we interprete /x> in relativistic QFT as position eigenstate?And by the way what is the difference between /x> and /1x>=Phi(field operator)(x)/0>?

In QM by virtue of wave function we calculate any things. But in QFT it seems that there is a lacking of notion of wave function.I do not understand why QFT still goes well(it is a good theory to calculate any things)?

What would you say is essential reading for those of us who want to understand how exactly is QFT benefiting from QI? Can anyone give a summary of what is happening, and where to start reading? (at postgraduate/entry-research-level).

Good day, I'm starting my master in physics, and it's time for me to choose my courses. I will take one or two of the following three courses, which are: Statistical Physics, QFT and General relativity. Now, I'm finding it very hard to decide as on the one hand, I'm interested in QFT and...

I was reading about the renormalization of ##\phi^4## theory and it was mentioned that in order to renormalize the 2-point function ##\Gamma^{(2)}(p)## we add the counterterm : \delta \mathcal{L}_1 = -\dfrac{gm^2}{32\pi \epsilon^2}\phi^2 to the Lagrangian, which should give rise to a...

Hello. I am trying to learn quantum field theory. I am crazy about it but I have some problems in my study. I use An Introduction to Quantum Field Theory by Peskin and Schroeder. It is said that the book is easier to learn than other books. However, I have to spend a lot of time in computing...

Hi! I know some theorists believe all quantum fields and gravitational field are different aspects of one universal field. What does that formally (e.g. mathematically) mean "to be different aspects of" and how can one prove, let's say, fields A and B are different aspects of C? By the way, I...

According to Bell's theorem quantum mechanics is not local.How can we combine it with Special Relativity which is local and gives us another successful theory?

When we touch something, will there always be a layer of air between us?

How did you find PF?: Google I know how to express Hamiltonian for scalar field written in field operators through the raising and lowering momentum operators, but I can't figure out how to do the same for the number of particles written in field operators: the 1/2E coefficient within the...

I am particularly interesting in QFT, and I am going to be a graduate student in quantum optics and quantum information this autumn. Strangely, I find that there is no courses for QFT. After all, I though QFT are about quantum and field, and quantum optics are about quantum and field, too...

Hey, applied maths and physics student here. I started wondering recently what the meaning of measurement was in quantum mechanics, and I remembered that I had once heard of the bohmian interpretation which challenged the impression I had so far (which was that hidden variables had been...

Is it possible to determine the amount of zero-point energy contributed by all fields below the Planck energy cutoff?

Hi everyone, I'm new to PF and this is my second post, I'm taking a QFT course this semester and my teacher asked us to obtain: $$[\Phi(x,t), \dot{\Phi}(y,t) = iZ\delta^3(x-y)]$$ We're using the Otto Nachtman: Elementary Particle Physics but I've seen other books use this notation: $$[\Phi(x,t)...

Hi everyone, I'm taking a QFT course this semester and we're studying from the Otto Nachtman: Texts and Monographs in Physics textbook, today our teacher asked us to get to the equation: [Φ(x,t),∂/∂tΦ(y,t)]=iZ∂3(x-y) But I am unsure of how to get to this, does anyone have any advice or any...

I've been slowly grinding away with what I can about quantum mechanics and QFT. I'm not sure how far I've gotten but I've come up against a bit of a roadblock concerning how the relativity of simultaneity applies in QFT with specific reference to the outcome of Bell tests. My misunderstanding...

Non-relativistic Bremsstrahlung is discussed classically in Rybicki “Radiative Processes in Astrophysics” where Larmor’s formula is used to find the power radiated in a collision between an electron and a Coulomb field. The Fourier transform of the pulse allows for a description of the pulse in...

Consider the process e^-\rightarrow e^-\gamma depicted in the following Feynman diagram. The spin-averaged amplitude with linearly polarised photons is \overline{|M|^2}=8\pi\alpha\left(-g^{\mu\nu}+\epsilon^\mu_+\epsilon^\nu_-+\epsilon^\mu_-\epsilon^\nu_+\right)\left(p_\mu p^\prime_\nu+p_\nu...

I'm looking forward to have a better understanding of the polarization vector in quantum field theory in order to solve a particular problem. In class and in several textbooks I see that ##s^\mu=(0,\vec s)## and ##|\vec s|=1##. Are polarizations vectors defined to have no temporal component in...

I am getting started in applying the quantization of the harmonic oscillator to the free scalar field. After studying section 2.2. of Tong Lecture notes (I attach the PDF, which comes from 2.Canonical quantization here https://www.damtp.cam.ac.uk/user/tong/qft.html), I went through my notes...