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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 this tag for many-body quantum-mechanical problems and the theory of [tag:particle-physics]. Don’t combine with [tag:quantum-mechanics].

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Path integral measure in Chern-Simons/WZW correspondence

The relationship between 3d Chern-Simons theory on the product of the disk and the real line ($D\times \mathbb{R}$) and the chiral WZW model on $S^1\times \mathbb{R}$ was shown in Elitzur et al Nucl....
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Why Proca Term forbidden in Schwinger Model?

In my QFT Lecture we considered the Schwinger model with a Proca term. Solving the eom for the Stueckelberg field and plugging it back into the original Lagrangian, we receive an effective Lagrangian ...
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1answer
147 views

How does the Fine Structure Constant Vary with Energy?

Like my topic, how does the fine structure constant vary with energy? I looked it up and found: $$\alpha_{eff}(q^2) = \frac{\alpha}{1-\frac{\alpha}{3\pi}\ln(\frac{-q^2}{Am_e^2})}$$ , where $\alpha^{-1}...
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What are “the correct spin operators” mentioned in the book “Quantum Field Theory” by Lewis H. Ryder?

In subchapter $2.7$ ("The relevance of the Poincaré group", page 63), to be found in this link, Ryder writes: The correct spin operators are rather complicated in form and the interested reader is ...
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18 views

Integration measure in quantum field theory conventions

In my university QFT course the lecturer used a convention for the integration measure with a factor $1/(2E(\vec{k}))$. For instance in $$\phi(x) = \int \frac{d^3\vec{k}}{2(2\pi)^3E(\vec{k})}(a^\...
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Feynman Parameters vs Passarino-Veltman reduction

I have computed the following one-loop integral: $$\int \frac{d^dp}{(2\pi)^d} \frac{p^{\mu}p^{\nu}}{(p+k)^2p^2}.$$ Using both Feynman Parameters and the Passarino-Veltman reduction. However, while I ...
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Maximal Parity violation in Weak interactions

In 1956 Lee and Yang proposed parity violation of the weak interactions to explain the $\theta-\tau$ puzzle. The following year, 1957, Madam Wu and collaborators found that in the $\beta$ decay of ...
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157 views

Transition amplitude for QED+QFD+QCD interactions

As I understood my Feynman diagrams are nothing more like pictures for the transition amplitueds (up to some orders). For this we introduce a interaction vacuum state $|\Omega\rangle$ then we are able ...
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32 views

Integral and Wick rotation (Srednicki ch75)

I was reading chapter 75 of Srednicki's QFT book and I ran into this statement. To determine the value of its integral, we make a Wick rotation to euclidean space, which yields a factor of i as ...
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Comparison of two Yukawa theories

I consider vacuum polarization diagram in two different Yukawa theories: with scalar coupling $g\bar{\psi}\phi\psi$ and pseudoscalar coupling $ig\bar{\psi}\gamma^5\phi\psi$. I am interested in ...
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Integral calculation

I deal with the following integral from Landau's QED (see 520 page): $$I^{\mu\nu}=\int_{-1}^{+1}d(\cos\theta)\frac{f^{\mu}f^{\nu}}{1-\cos\theta},$$ where $f=(0,\,{\bf p}-{\bf p}_{-})$ is space-like 4-...
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QCD vs. QED gauge invariance

Trying to understand the difference between QED and QCD gauge invariance treatment I found the following paper: https://arxiv.org/pdf/1101.3425.pdf I have the following questions: 1) I understand Eq....
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What is the high-energy/superstring analogue of wave function?

Chapter 12 of Beckers' book about superstrings and m-theory lists several deep dualities between low energy gauge theories and high energy superstring theories. I am only at the Chapter 2, that is why ...
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Does every regularization/renormalization approach gives running coupling constants?

I'm studying different tools for regularization and renormalization. Until now I vaguely understand 1) the wilson approach to renormalization where one thinks of the theory as essencially effective ...
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In what ways is eternal inflation less certain than standard inflation? [on hold]

Eternal inflation is the idea that inflation could be eternal due to the effect of quantum fluctuations of the inflaton field. Why do some cosmologists accept inflation, but consider eternal ...
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Why are there two magnon propagators in Ferromagnetic system?

I am confused that the authors of ref.[1,2] defined two magnon propagators in the ferromagnetic system with magnon-phonon coupling (which is similar to electron-phonon coupling). They defined ...
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1answer
153 views

What's the reasoning behind propagators definitions (specifically fermionic propagators)

I'm studying QFT by David Tong's lecture notes. When he discusses causility with real scalar fields, he defines the propagator as $$D(x-y)=\left\langle0\right|\phi(x)\phi(y)\left|0\right\rangle=\int\...
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How do anomalies affect the field equations of motion?

I find anomalies an extremely unintuitive subject, because they're studied so indirectly. In the standard textbook presentation, one computes an abstract quantity that should be zero classically (say, ...
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1answer
112 views

Is there confinement in the Gross-Neveu model?

The Gross-Neveu model is a simple quantum field theory in 2 space-time dimensions that is considered a toy model for QCD, in the sense that it realizes asymptotic freedom, chiral symmetry breaking ...
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1answer
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How do we see that the axion is a pseudoscalar?

The axion is the pseudo-Goldstone boson associated to the breaking of the conjectured Peccei-Quinn Abelian symmetry. The axion couples to the SM gauge fields in a CP-invariant manner (e.g. $aF\tilde F ...
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1answer
25 views

Calculating Field moments of two mode squeezed state

I am reading through a paper (EDIT: Paper is here) and I actually want to rigorously go through their calculations. I am having some issues, For a two mode squeezed state given by: $$|\psi\rangle = ...
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QCD gauge invariant amplitude?

In order to keep the correct degrees of freedom (which are 2) for massless gauge fields one imposes, $$p^\mu \epsilon_\mu = 0 \tag1$$ Together with the gauge redundacy/equivalence relation, $$\...
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Non-relativistic limit of particle decay

Let us consider the theory with scalar coupling $g\bar{\psi}\phi\psi$. For the decay process $\phi\rightarrow \bar{\psi}\psi$ one can write down the following amplitude: $$\mathcal{M}=ig\bar{u}(-p_{-})...
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Angular momentum for asymptotic states in black hole spacetime

Consider a massless KG field propagating in a gravitational collapse spacetime which produced a black hole. Neglect backscattering for a moment. In that case, when asymptotic quantization is ...
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Different Schwinger-Dyson Equations

In the literature on QFT there are a lot of different equations that are all called "Schwinger-Dyson equation" so I wanted to know how are they related and if they have proper names. The first ...
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1answer
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The relation between decay width and vacuum polarization

Recently I have found this problem: My question: Does the relation $\mathrm{Im}\,\Pi(M^2)=-M\Gamma$ work for arbitrary theory or it should be modified?
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Does the $\frac{4}{3}$ problem of classical electromagnetism remain in quantum mechanics?

In Volume II Chapter $28$ of the Feymann Lectures on Physics, Feynman discusses the infamous $\frac43$ problem of classical electromagnetism. Suppose you have a charged particle of radius $a$ and ...
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Electroweak phase transition and finite temperature field theory formalism

We do our calculations in standard quantum field theory at zero temperature where we can derive pole mass and renormalized mass and ... Due to my understanding, pole mass is independent of any energy ...
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1answer
32 views

u-channel in $gg \rightarrow u\bar{u}$

I've seen that for the QCD process $gg \rightarrow u\bar{u}$, where $g$ is a gluon and $u, \bar{u}$ are the up quark and the corresponding antiquark, there is s, t and u channels. I perfectly ...
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1answer
148 views

Matter effects in neutrino oscillation

The neutrino oscillation probability in matter is given as: where Now what I do not understand is that "As the energy increases, the probability of oscillation within the sun through the matter ...
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24 views

Is this how superposition works? [on hold]

I know everywhere contain fields and one field can interact with another field producing interaction which is excitation of some fields so I think when there is a particle it is an excitation of many ...
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1answer
154 views

Trying to work out the CP-transformation property of the Higgs potential

The parity transformation property of a complex scalar field $\phi(x)$ is given by: $$P\phi(t,\textbf{x}) P^{-1}=\eta_P\phi(t,-\textbf{x})$$ where $\eta_P=\pm 1$. The charge conjugation property of a ...
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128 views

Nature of Spin in QFT

If the orbital angular momentum of an electron in an atomic orbital is associated with (generated by) an asymmetry in the orbital wave function, is it also the case that the intrinsic spin of a free ...
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1answer
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Beta function in the Standard Model

In Srednicki's textbook "Quantum Field Theory", Problem 89.4 asks us to compute the leading terms in the beta function for each of the three gauge couplings of the Standard Model. These gauge ...
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1answer
58 views

Weinberg's Coleman-Mandula theorem proof sufficient condition for isomorphism?

In Weinberg's QFT Volume 3 book on Supersymmetry, he presents his own proof of the Coleman-Mandula theorem. As part of the proof, he proves that the only possible internal symmetry generators must ...
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1answer
150 views

Why do we have freedom to choose a renormalization scale in massless QFT theories?

I thought that the freedom to choose renormalization conditions arises from the freedom to choose the arbitrary renormalization parameters. Let me exemplify this in a Massive $\phi^4$ scalar theory ...
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Measuring the lorentz transform generators $J$, $K$, and providing evidence that photons have no internal continuous d.o.f

I am reading Weinberg's first QFT book. We looked for (and I suppose found) unitary representations of the Lorentz group: $$U(\Lambda) = 1 - i (\vec{\theta}\cdot\vec{J}-\vec{\eta}\cdot \vec{K})$$ ...
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1answer
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Question about differentiating wrt. momentum in Srednicki chapter 14

I am having a bit of trouble following a simple integral from the book on QFT by Mark Srednicki - free draft can be accessed at http://web.physics.ucsb.edu/~mark/qft.html - and I was hoping you could ...
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Higgs-Mechanism: Why are gauge boson masses not protected by gauge symmetry

In non-spontaneously broken QFT like QED the gauge bosons cannot have a mass due to gauge symmetry (follows from Ward identity). Also they have only 2 polarizations. However in a spontaneously broken ...
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1answer
39 views

Hamiltonian of a quantum heat bath

I have seen the Hamiltonian for a heat bath written as: $$ H_B = \hbar \int_0^\infty \omega b(\omega)^\dagger b(\omega) d\omega $$ I was hoping to understand this equation better. This suggests that ...
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Optical theorem in $\phi^4$: which poles contribute to discontinuity in Feynman amplitude?

Section 7.3 ("The Optical Theorem") in Peskin and Schroeder's QFT text contains a leading order verification of the optical theorem in $\phi^4$ theory by calculating the (discontinuity across the ...
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10answers
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Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. However, I wonder, is this actually a duality? At the most fundamental level, we 'know' ...
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1answer
173 views

Optical theorem in QFT

I've been working with the Optical theorem in the case in which final and initial states are equals and I have the following doubt. Let's write the scattering matrix $S$ as: $$S = 1 + i·T \tag1$$ ...
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Parton distribution function in terms of Fock space kets

To my understanding, I can (at least, formally) express the (unnormalized) PDF for a certain constituent of a composite state as $$ f(x)=f\left(\dfrac{k}{K}\right)=\sum_j m_j^{(k)}|\langle\psi_j^{(k)}|...
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1answer
60 views

QFT Matter Fields and Anti-Matter Fields

In QFT is it the case that the electron matter field and anti-electron matter field (using the electron as a specific example) are truly distinct physical fields versus different excitation modes of ...
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1answer
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How to prove the equivalence of two different difinitions of S-operator?

I read there are two definitions about S-operator: The first one (e.g (8.49) in Greiner's Field Quantization) is: $$S_{fi}\equiv \langle \Psi_p^{-}| \Psi_k^{+}\rangle$$ where $|\Psi_p^{-}\rangle$ is ...
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Quantum field theory books for laymen? [duplicate]

I was watching David Tong's lecture on quantum field theory here and even as an almost complete beginner to university level physics, I understood most of it and it has made me very interested in ...
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1answer
55 views

What people mean by “state evolving with the interacting/free theory”?

This is a quite basic question but I confess it is something I didn't get up to this point. When defining the Moller operators and hence the $\cal{S}$-matrix one usually considers "states $\Psi$ ...
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1answer
127 views

Feynman $i\varepsilon$-prescription in path integral by adding an imaginary part to time

It is known that the well-definiteness of the path integral leads to the Feynman's $i\varepsilon$-prescription for the field propagator. I've found many ways of showing this in the literature, but it ...
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Casimir force between two plates

Literature recommendation for deriving the Casimir effect and attractive force between 2 parallel plates.