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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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Vacuum polarization contribution to magnetic moment

Where I can find the calculation of muonic (or electronic, it does not matter) vacuum polarization contribution to the anomalous electron magnetic moment? I mean the diagram (c):
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How to interpret this construction of the states in QFT?

Non-Relativistic Quantum Mechanics To make this question clear it might be useful to contrast with non-relativistic quantum mechanics. In any quantum theory, the states of a system are unit rays in ...
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Kinetic term for a Majorana fermion in curved Weyl geometry

I am trying to write the action for a Majorana fermion on a curved Weyl-gravity background. Since I am considering a fermion in curved space, the tetrad formalism is appropriate and the kinetic term ...
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Why can't large momentum effective theory be applied to fragmentation function?

Large momentum effective theory was proposed in 2013 by Prof. Xiang-Dong Ji. The idea is to numerically solve PDF in lattice QCD via so-called quasi-PDF in finite momentum frame. Such method is ...
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The flip of the spin (Problem 11.6(b) in Schwartz's QFT)

I am asking a question regarding the following problem: For the non-relativistic limit, choose explicit spinors for a spinor at rest. Show that $\bar\psi_s\gamma^\mu\psi_{s'}$ vanishes unless $s=s'...
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What is the 't Hooft determinant?

The 't Hooft vertex/determinant is somehow generated by instantons and is responsible for the generation of mass gap in pseudo-Goldstone bosons, such as an axion. For example, the complex Peccei-...
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Question regarding Little group for massless particle

Consider a particle with velocity $P = (1,1,0,0)$. The little group for it is E(2) (same as). Here, in this book by YS KIM, he talks about this little group in section 2.3. He says in addition to E(2)...
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Are there Rules for 'Splitting' Feynman Diagrams?

I was talking with a mathematician colleague and promised to look up a concept in QFT for them but am not sure what they were referring to. They were referring to rules named after two people (both ...
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What is the closed form of the following integral?

I want to know the closed form of the following master integral in (any) $D$ dimension \begin{equation} \int\frac{d^D k}{(2\pi)^D}\frac{1}{k^2(k+r)^2(k+p)^2}. \end{equation} The references that I can ...
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Physically, why don't we care about representations that differ only by a similarity transformation?

I was looking at how to derive the (1/2, 0) representation of the Lorentz group when acting on fields. Specifically, I'm interested in understanding the logic behind replacing the "symbols" $A,B$ with ...
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Is there a connection between these two results on soft hair on black holes?

In 2016 Strominger, Hawking and Perry published the paper "Soft Hair on Black Holes" proposing new results that could have importance to the study of the black hole information problem. One ...
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What´s the matter when the measurement device is destintegrated in a quantum system? Is there any way to descript this situation?

Nuclear desintegration is a phenomenon that increases wiht time, and even at least as far as we know the protons end up disintegrating. What happens if the source of measurement disintegrates? By the ...
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Why is Chern–Simons theory in 2+1 dim is equivalent to scalar field

My profs keep telling me Chern–Simons in 2+1 dimensions is equivalent to scalar field in same dimensions. Can someone explain whether is true or not ? If so, how ? Edit: There's a paper Jackiw, ...
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Contour Integration in Schwartz

In Matthew Schwartz's QFT text, on page 39, he has the following contour integral: $$\int_{-\infty}^{\infty}dk\frac{e^{ikr}-e^{-ikr}}{k+i\delta }.\tag{3.63}$$ This can be split into two terms, one ...
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Understanding irrelevant operators in Wilsonian RG

I had always understood irrelevant operators as operators whose coefficients got smaller at lower energy scales, but there's a passage from Schwartz's Quantum Field Theory and the Standard Model which ...
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Harnessing molecule vibration energy

Disclaimer: I am learning physics for fun, please dont kill me but explain where I am wrong. As I understand all molecules have a lowest energy state in which they posses some amount of momentum even ...
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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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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? [closed]

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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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? [closed]

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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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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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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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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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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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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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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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.