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Questions tagged [quantum-field-theory]

Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use ...

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Converting a general QFT state to another inertial of light-cone reference frame

Assume, in a certain reference frame, a relativistic QFT at time $t=0$ is in the state $$ \hat{\Psi}(t=0) |vac\rangle \quad, $$ where $$ \hat{\Psi}(t) = \operatorname{e}^{-i\hat{H}t} \sum \limits_{n=1}...
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Sign in derivative/momentum when computing Feynman rules

I've see that when we have an interaction with derivatives, in order to get the corresponding vertex you have to apply the prescription $i\partial_\mu \rightarrow p_\mu$, but has this prescription a ...
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Thermal Quantum Field Theory methods

I have been reading about the various techniques that have been employed to study quantum field theories near equilibrium. It seems that the two main ways are the Schwinger-Keldysh (SK) and the ...
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Analytic Continuation in QFT

I'm having some trouble with a problems from Ramond's book "Field Theory, A Modern Prime". First the problem asks to do a wick rotation in the integral $$\tag{1}\label{1} i\int_{-\infty}^{+\infty}{dt\...
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Problem with converting Integral to Gamma functions (from HQET heavy quark self-energy diagram)

In the calculation of HQET radiative correction, I came across the Equation: $$\int_0^{\infty}d\lambda ~ \lambda^{-\epsilon}(\lambda+\omega)^{-\epsilon} = \frac{1}{2\sqrt{\pi}}\Gamma(\epsilon-\frac{1}{...
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32 views

One-loop correction to triple gluon vertex in QCD

I'm trying to calculate a one loop correction to the 3 gluon vertex, which is given by a circular correction, and another that's due to the 4 gluon vertex. However I'm unsure how the ghost fields ...
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Can we ever “measure” a quantum field at a given point?

In quantum field theory, all particles are "excitations" of their corresponding fields. Is it possible to somehow "measure" the "value" of such quantum fields at any point in the space (like what is ...
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Commutator of a quark current

In Quantum Chromodynamics, when we take the limit in which the u, d and s quarks have no mass, there exists a global symmetry $G \equiv SU(3)_L \otimes SU(3)_R$ in flavour space. The corresponding ...
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Singular behavior of pure gravity

Can anyone plese explain what means singular part of partition function for pure gravity? Let me specify my question. I am dealing with 2D quantum gravity and starts from path integral formulation of ...
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2answers
68 views

Should Hamiltonians in quantum field theory be linear operators?

The usual structure of quantum mechanics imposes that Hamiltonians are linear operators. I am not sure if this really holds in quantum field theory. Do non-linear Hamiltonian operators really make ...
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50 views

Closed set of operators under renormalization

While reading the article http://inspirehep.net/record/61135, I came across the concept of "closed set under renormalization". The definition they give is the following. In any renormalizable field ...
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Normalization for the overlap $\langle \phi_a | 0 \rangle$

This question is related to my previous post here. According to Wienberg's Volume I (9.2.9), we have the result $$ \langle \phi_a | 0 \rangle = \mathcal{N} \mathrm{exp}\left( - \frac{1}{2} \int d^{3}\...
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28 views

High-energy effective field theory

Usually when one speaks of effective field theories, one is looking to integrate out certain fields which are typically heavy in comparison to the regime of interest. That is one has a theory at a ...
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35 views

Mode Expansion in Klein-Gordon QFT

I have a confusion regarding the mode expansion of the Klein-Gordon field theory. I am following Peskin and Schroeder. My questions are about how we formally get to the expansion of the KG QFT in ...
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1answer
36 views

Proving equivalence of first and second quantisation (Pathria's way)

I'm trying to solve problem 11.1 form Pathria R. K. & Beale P. D. - Statistical mechanics book (the hyperlink will get you straight to the page of the problem). The point (b) is to show the ...
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Deriving Ward identity directly from a given formula for the conserved current only using the equal-time canonical commutation relation

I have a very technical question on deriving a Ward identity directly from a given explicit form of the "conserved current". Let me emphasize that I do not start with an apriori knowledge on the ...
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1answer
30 views

Couplings in the SYK model

I have read several times by now that the couplings in the SYK model are drawn randomly from a gaussian distribution. I was wondering what exactly is meant by that. To elaborate, when I compute an ...
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1answer
28 views

Can the Hermitian conjugate of a column vector still be column vector?

From what I understand, contravariant vectors are represented by column vectors, and covariant vectors are row vectors. So for a QED current, say $j ^ { \mu } = \overline { \psi } \gamma ^ { \mu } \...
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Explicit forms of lepton fields

In Srednicki's textbook "Quantum Field Theory", Eq. (88.17) reads \begin{equation} T^{3}\nu = + \frac{1}{2}\nu, \hspace{0.3in} T^{3}e = - \frac{1}{2}e, \hspace{0.3in}T^{3}\overline{e} = 0 \end{...
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1answer
33 views

Frequency gap between neighbouring spectral lines

According to classical theory the atomic line spectra are discrete and their frequencies quantized. Have the newer quantum theories changed anything since then, giving some other expressions for the ...
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Feynman rule for 3-gluon vertex

I want to obtain the Feynman rule for the 3-gluon vertex, but looking at the result I don't really know how to tackle it. The relevant term in the Lagrangian is \begin{equation} \mathcal{L}_\text{...
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What fields of physics that use abstract math concepts can undergraduates start to look into? [on hold]

I’m In my Junior year of my math/physics major and I’m interested in pursuing a graduate degree in mathematical physics. My university requires a Sr Thesis for graduation and I would love to do it on ...
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Where does Field Theory come from?

About my background: I'm currently a 4th year undergrad, and planning to do a PhD in theoretical physics. I think I have a decent understanding of basic physics, and I know how to do calculations in ...
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1answer
30 views

Tricks to evaluate expectation values for operator strings in second quantisation

I am taking a course in many-body quantum mechanics. Often, I have to evaluate expectation values on strings of creation/annihilation operators. I was told that to evaluate these, I should use the (...
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Questions on how Wilson loops relate to field & charge conservation, and lattice QFT

The path-ordered exponential from which the Wilson loop is traced is, crudely, $$ \prod (I+ A_\alpha dx^\alpha) = \mathcal{P}\,\mathrm{exp}(i \oint A_\alpha dx^\alpha )$$ which returns a matrix $\...
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1answer
49 views

Composite particles and Weinberg Witten (WW) theorem

I am quite familiar with the proof of Weinberg Witten (WW) theorem. One major result which follow from WW is that the graviton cannot be a composite particle. I have 2 questions here: How do we tell (...
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1answer
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Is it possible to define an energy momentum tensor for classical point particles from a QFT?

I have a question about the semi-classical limit of a QFT that so far I have never been able to solve. Let's start with a second quantized Klein-Gordon field with Lagrangian $$\mathcal{L}(\phi)=\frac{...
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1answer
56 views

Time reversal transformation of the complex scalar field

consider a complex scalar field $\phi$ $$\phi(t,x)=\int\frac{d^3k}{\sqrt{2\omega_k(2\pi)^{3}}} \big(a_ke^{i\vec{k}\cdot\vec{x}-i\omega_kt} +b^\dagger_ke^{-i\vec{k}\cdot\vec{x}+i\omega_kt}\big)$$ By ...
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3-particle phase space in $d$ dimensions

recently I came across a problem concerning the 3-particle phase space. I am trying to show, that the 3-particle phase space for massless particles with momenta $p_1$, $p_2$ and $k$ is given by $$ d\...
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0answers
30 views

Is one allowed to split path integrals in the Feynman-Vernon Influence theory

In QFT the propagator $J(t,t_0,x_f,x_i) = \langle x_f | U(t,t_0) | x_i \rangle$ fulfills the property $$ J(t,t_0,x_f,x_i) = \int_{-\infty}^{\infty}dx' J(t,t',x_f,x')J(t',t_0,x',x_i) $$ and can be ...
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3answers
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Is wave function collapse the only source of 'randomness' in QM? What about field fluctuations? Are these two even distinct?

Basically I want to know the validity of the statement, "All randomness originates from wave function collapse" or maybe "The only true random event is the collapse of wavefunctions" This seemed to ...
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Why does Bell's field theory model need to be stochastic on a space-time lattice?

In "Beables for quantum field theory", John Bell has presented a realistic interpretation of any fermionic quantum field theory, along the pilot-wave ideas. This model is formulated on a spatial lattice ...
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Dimension of gamma matrices in dimensional regularization

When performing loop integrals in theories containing Dirac fermions, one almost always confronts terms of the form $$\text{Tr}\left[\gamma^{\mu_1}\cdots\gamma^{\mu_n}\right].$$ For instance, in $d$ ...
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How to describe quantum mechanically that a particle falls into a black hole?

Consider a black hole spacetime originated by gravitational collapse, like the following Vaidya geometry $$ds^2=-\left(1-\frac{2M\theta(v)}{r}\right)dv^2+2dvdr+r^2(d\theta^2+\sin^2\theta d\phi^2).$$ ...
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Relative sign between Feynman diagrams

Let's suppose I have some decay process and my original particle $\psi$ can go to $\eta, \bar{\xi}$ or $\bar{\eta}, \xi$ (all fermions). Then, I will have 2 Feynman diagrams but, will be a plus or a ...
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Question regarding the degeneracy of vacuum state in various spacetimes

In a talk, it was mentioned that if one attempts to do quantum gravity in the following spacetimes (of any dimension), then the vacuum state has the following degeneracy. In $AdS$ - There is a ...
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QFT Path integral for Harmonic Oscillator derivation [closed]

I am currently working through Srednicki's QFT, and am stuck on a step he uses in Eq. 7.3 to derive the path integral for the harmonic oscillator. He writes $$H = \frac{1}{2m}P^2 + \frac{1}{2}m \...
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78 views

Weinberg operator question

Similar posts have been made on this site, but none of them seem to answer my specific questions. I am quite new to QFT (especially standard model) so these may seem trivial to you. We have the ...
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2answers
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Hawking said virtual particles can almost become real particles, following closed trajectories. Can someone explain to me?

Here's hawking quote from his latest book. Brief Answers to the Big Questions "When space-time gets warped almost enough to allow travel into the past, virtual particles can almost become real ...
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How to derive Lorentz invariant combo of momentum and energy?

I have a question regarding the derivation of the equation for the Lorentz-invariant combination of momentum and energy from Wigner. I believe I mostly follow the derivation of the Hamiltonian and ...
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What does the identity operator look like in QFT, written in momentum eigenstates? [duplicate]

This is a followup to a question I read recently: What does the identity operator look like in Quantum Field Theory? Out of curiosity, I was writing down what I figured to be the momentum basis ...
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2answers
49 views

Equivalence between $t$ and $u$ channels

Reading about QFT diagrams, I've seen examples like Bhabha scattering where the channel $u$ wasn't necessary due to the final states are distinguisable for being made of the different particles and ...
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0answers
40 views

What QFT is needed to understand the prediction of dark matter particles?

I am just starting to learn Quantum field theory. I want to understand how people go about with modeling the possible dark matter candidates like WIMPs, axions, etc. I wanted to know what QFT I need ...
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1answer
79 views

What is the transpose of Lorentz transformation under spinor representation?

Let $S$ be the Lorentz transfortmation under spinor representation, and from any quantum field theory textbooks, we know that $$ S^\dagger=\gamma^0S^{-1}\gamma^0 \\ S^{-1}=\gamma^0S^\dagger\gamma^0 $$ ...
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1answer
73 views

What is the difference between QFT and QED? [closed]

What is the difference between QFT and QED? In QFT electron is field quanta, what is electron in QED?
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Released energy through bubble nucleation

I am reading the paper by Coleman "Fate of the false vacuum: Semiclassical theory" which explains how bubble nucleation occurs in first-order phase transition in field theories. I will summarise the ...
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1answer
109 views

Particles, fluctuations and the quantum vacuum: is this right?

After answering a question on quantum fluctuations Could quantum fluctuations spawn real matter?, I got into conversation with E. D. Kramer (to whom thanks) and in the end it may be that we had a ...
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1answer
66 views

Symmetry factor in $\phi^4$ theory

I'm having trouble while trying to understand what the symmetry factor of a Feynman diagram really is. From books I get that it is a geometrical factor that you get by the number of ways in which you ...
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1answer
95 views

Paths contributing to the path integral measure in Gross' book

My question regards a comment D. Gross makes in his unpublished lecture notes about quantum field theory (the one with no chapter 1). In chapter 8 (path integrals) pag. 136, he reaches at the ...
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2answers
115 views

How do you derive a quantum field theory from a spacetime metric?

What are the first steps in converting a metric into a quantum field theory? I know roughly what to do once I have a pair of non-commuting operators, but how do I get to that point? Specifically, I'd ...