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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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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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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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1answer
31 views

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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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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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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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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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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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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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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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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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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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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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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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
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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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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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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1answer
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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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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
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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
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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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
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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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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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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Casimir force between two plates

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

Dealing with more complicated tree level feynman diagrams

Suppose I have a 2 -> 4 body process of the form Where all particles are scalar $\phi$ of mass $m$, dirac fermion $\chi$ of mass $M$ with interaction lagrangian $g\overline{\chi}\chi \phi$ . How does ...
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Faster ways of computing feynman diagrams

Obviously the machinery of QFT allows us to calculate processes, such as QED diagrams, to great precision, and whilst it is effective, it seems there are many processes that make calculations (say by ...
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Effective potential and radiation corrections

I'm a bit confused on the idea of adding corrections to the classical potential of $\phi^4$ theory in QFT. From what I understand is that one should add corrections to the potential in order to ...
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$ e^+e^- \longrightarrow \mu^+\mu^-$ probability density function of $\theta$ strange trend

I'm considering the process: $$ e^+e^- \longrightarrow \mu^+\mu^-$$ The cross section in the center-of-mass frame: \begin{equation} \left( \frac{d \sigma}{d \Omega} \right)_{CoM}= \frac{\alpha^2}{4 s}...
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When can you simplify the W boson propagator

I have seen in several sources that the propagator of the $W$ boson is: $$\frac{- i \left( g^{\mu\nu} - \frac{P^\mu P^\nu}{m_W^2} \right)}{p^2 - m_W^2} $$ But then in some calculations (usually ...
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How to grasp the limits of these two integrals? [duplicate]

I find some difficulty in understanding the limits of the two integral below (on Page 27 of Peskin & Schroeder's Quantum Field Theory): $$D(x-y)=\frac{1}{4\pi^2}\int_m^\infty d E \sqrt{E^2-m^2}e^{...
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How to solve this particular problem of Wick's theorem?

So I know the basics of Wick's theorem, but unsure about how to solve this time ordered product of a term that involves normal ordering. Is it just simply the sum of all possible contractions, but no ...
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A proof that Heisenberg's and Euler Lagrange's equations are equivalent in QFT [closed]

I asked this before (link, link) but I think people didn't understand what I was asking, so I am going to try again . Thanks for everyone that helped so far. In QFT, Heisenberg's equation is ...
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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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Why is the imaginary part of the Breit-Wigner propagator given by the total decay width?

The optical theorem links the imaginary part of the forward scattering amplitude to the total decay width of a particle: $\mathrm{Im}\,M_{i\to i} = m\Gamma_{tot}$. Here $\Gamma_{tot} = \frac{1}{2m} \...
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1answer
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Explicit quantization of free fermionic field

The canonical quantization of a scalar field $\phi(x)$ can explicitly be realized in the space of functionals in fields $\phi(\vec x)$ (here $\vec x$ is spacial variable) by operators \begin{eqnarray} ...
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Is the mass of a particle determined by the extent to which it interacts with other particles? [closed]

This is more a question about the Higgs field than anything else. If you were to take, for example, a neutrino and send it out into empty space how could you determine that it has a mass in the first ...
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Touching is a Pauli exclusion principle or electrostatic force? [duplicate]

According to quantum field theory touching is an electrostatic repulsion between electrons or the Pauli exclusion principle? How can physicists distinguish these two phenomena if they give the same ...
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What substitutions are allowed within time-ordered products?

I always thought of the time-ordering in QFTs as an explicit operation. Meaning the time-ordering "operator" just takes everything I write inside it and shuffles the operators around until they are in ...
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Zero-Temperature Limit of Matsubara Sums

Consider the fermionic Matsubara sum for $$\frac{1}{\beta}\sum_n G^2(k,\omega_n) = \frac{1}{\beta}\sum_n \frac{1}{(i\omega_n - \epsilon_k)^2}$$ where $G(k,\omega_n)$ is the free fermion Green's ...
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Are there any known models with limit cycles in their RG flow?

The text-book presentation of the renormalization group (RG) leaves one with the impression that all systems will eventually flow to a fixed point. This is somewhat enforced by the phenomenological ...