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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68 views

One question about Weinberg's derivation of arbitrary spin fields expressions

In his book "QFT" (vol. 1) Weinberg writes the expression for an arbitrary spin massive field: $$ \hat {\Psi}_{a}(x) = \sum_{\sigma = -s}^{s} \int \frac{d^{3}\mathbf p}{\sqrt{(2 \pi)^{3}2 ...
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votes
3answers
412 views

why cannot fermions have non-zero vacuum expectation value?

In quantum field theory, scalar can take non-zero vacuum expectation value(vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory ...
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0answers
36 views

Regulating a particular function

I am interested in computing the integral of this function: \begin{align} \int_0^\infty\frac{2du(u^2+1)}{(1-e^{2\pi u})}, \end{align} which of course at first sight, does not converge. But in QFT ...
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1answer
62 views

can interaction between a massless fermion and external sourse exist?

For example, let's consider the electromagnetic interaction between a massless fermion and a electromagnetic externel sourse $A^\mu$, then the lagrangian is ...
3
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1answer
68 views

'There shall be reheating' and other inflation-related questions [closed]

I've some basic questions about inflation: What is reheating exactly? What triggered the reheating? Is it something that one pulls out of a hat? Through which force did the decay of the inflation ...
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1answer
118 views

Lorentz transformations of fields evaluated at a point

I'm am sure that I must be missing something very simple, so apologies in advance. Considering the Lorentz transformation $\Lambda$ of a spinor fields, for the plane-wave solution $u(p)$, I cannot ...
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1answer
73 views

Fermion propagator is not a Grassmann-odd object?

Is the following differentiation correct: $$ \frac{\delta}{\delta\eta\left(z\right)}\int d^{4}yS_{F}\left(z-y\right)\eta\left(y\right) = S_F\left(z-z\right)$$ where $\eta$ is a Grassmann-valued ...
4
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1answer
129 views

Anti-symmetric forms on Dirac spinors

In order to describe invariant forms on Dirac spinors $S$ one can find trivial subrepresentations in $S \otimes S$. If we use $S \cong (1/2, 0) \oplus (0, 1/2)$ then \begin{multline} [(1/2, 0) ...
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1answer
58 views

Normalization of $\langle p_1 p_2 \vert p\rangle$ in RelQM and NonRelQM

Suppose a particle p of three momentum $\vec p$ decays into two particles of 3-momentum $\vec p_1$ and $\vec p_2$. I know the question might sound stupid but right now my brain is full stop: Is the ...
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1answer
71 views

Is $\langle k \vert k_1k_2\rangle=0$

Using that $$ \vert k_1k_2\rangle = a^\dagger({\bf k_1})a^\dagger({\bf k_2})\vert 0 \rangle$$ and the commutation relations $$[a({\bf k}),a^\dagger({\bf k'})]=(2\pi)^32\omega\delta^3(\bf {k}- \bf ...
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1answer
45 views

A question about propagator of Maxwell field in different gauge

The propagator of Maxwell theory is different, depending on the gauge fixing procedure used. Then why will the S-matrix elements be the same for the same process in different gauges?
3
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1answer
115 views

References on $C^{*}$-algerbas, $W^{*}$-algebras and Quantum Theories

I would like to know some references regarding $C^{*}$ and $W^{*}$-algebras and quantum theories. I'm interested in concrete physical applications, models and problems. Here it is the list of ...
5
votes
0answers
127 views

Functional integral aproach for Feynman rules

I am familiar with the basic ideas of quantum field theory but I feel uncomfortable when I have to derive Feynman rules by myself for a given action (for example in non-linear sigma models or ...
2
votes
1answer
287 views

Feynman propagators for scalar fields

If there are few massless scalar field, are the propagators of those different massless scalar fields indistinguishable?
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2answers
293 views

What forbids the existence of a $\lambda (A^\mu A_\mu)^2$ term in the Stueckelberg action?

In QFT, the Stueckelberg "trick" is often used to show how one can write a fully gauge invariant Lagrangian out of one that is not. For example, if we have $\mathcal{L} = ...
3
votes
1answer
203 views

Lagrangian density of an interacting real scalar field theory

Srednicki writes the Lagrangian density of an interacting scalar field theory as $$ \mathcal{L} = -\frac{1}{2} Z_\phi \partial^\mu \phi \partial_\mu \phi -\frac{1}{2} Z_m m^2 \phi^2 + \frac{1}{6} Z_g ...
9
votes
1answer
426 views

How to determine if an emergent gauge theory is deconfined or not?

2+1D lattice gauge theory can emerge in a spin system through fractionalization. Usually if the gauge structure is broken down to $\mathbb{Z}_N$, it is believed that the fractionalized spinons are ...
4
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1answer
112 views

Allowed interactions in bosonic string theory

In a quantum field theory, only a finite set of interactions are allowed, determined by the Lagrangian of the theory which specifies the interaction vertex Feynman rules. In string theory, an ...
8
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1answer
405 views

Nambu-Goldstone bosons from a quantum anomaly symmetry breaking?

We know that: Nambu-Goldstone bosons come from Goldstone theorem: a spontaneous (continuous)-symmetry breaking of the system leads to massless scalar modes. quantum anomaly: is the anomalous ...
2
votes
3answers
219 views

Green's function for adjoint Dirac Equation

If $S_F(x-y)$ is the Green's function for the Dirac operator $(i\gamma^\mu\partial_\mu-m)$, that is, I assume the following matrix equation holds: $$ (i\gamma^\mu\partial_\mu-m)S_F(x-y)=i\delta(x-y) ...
0
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0answers
147 views

Understanding Bose enhancement in reheating

I'm struggling to understand the Bose enhancement in reheating. I've read that: At the end of inflation, the inflaton field, $\phi$, is something like a condensate with excitations of a single ...
2
votes
1answer
175 views

Is there a simple explanation for Schwinger's relation $g=2+\frac{\alpha}{\pi}+{\cal O}(\alpha^2)$ for the $g$-factor of the electron?

Schwinger has on his grave (it seems) the relation between the g-factor of the electron and the fine structure constant: $$g~=~2+\frac{\alpha}{\pi}+{\cal O}(\alpha^2)$$ Did Schwinger or somebody ...
9
votes
1answer
158 views

The difference between $\mathcal{N}=2$ short multiplets and BPS states

I have some questions about the construction of $\mathcal{N}=2$ supermultiplets for chiral matter. I know that the supermultiplet should not include spin one states since they are always in the ...
4
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2answers
131 views

QCD mass gap finite temperature

QCD has a mass gap. Does heating up QCD to a finite temperature change this fact, or is it a property which is independent of temperature?
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1answer
130 views

Renormalizing composite operators

Consider the QED Lagrangian, \begin{equation} {\cal L} = \bar{\psi} ^{(0)} ( i \partial_\mu \gamma^\mu - m ) \psi ^{(0)} - e A _\mu ^{(0)} \bar{\psi} ^{(0)} \gamma ^\mu \psi ^{(0)} - \frac{1}{4} ...
7
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1answer
233 views

Generator of local symmetries

Let us only consider classical field theories in this discussion. Noether's theorem states that for every global symmetry, there exists a conserved current and a conserved charge. The charge is the ...
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0answers
57 views

Zero Energy States in 2D Systems

Since we are on a planar system (2D system) the massless Dirac equation reads $$\vec{\alpha}\cdot(\vec{p}-e\vec{A})\psi_E=E\psi_E$$ Here Dirac matrices are Pauli matrices ($\alpha^1=-\sigma^2$ , ...
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0answers
81 views

Scattering theory of Dirac equation in curved space-time in presence of a strong magnetic field

What is the exact solution of the Dirac equation in curved space-time in the presence of a strong magnetic field? The solution should be in momentum space for simplicity to calculate scattering cross ...
1
vote
3answers
229 views

Can virtual particles, in particular gravitons, interfere?

Question 1. Can virtual particles, in particular gravitons, interfere? Virtual particles are created and annihilated in a distance too small and a time too short to be measured. Their existence is ...
6
votes
2answers
524 views

The Fifth Gamma Matrix

This is regarding $\gamma^5$, the fifth gamma matrix in quantum field theory. I know its defining properties, namely, $$\gamma^5= -i\gamma^0 \gamma^1 \gamma^2 \gamma^3 $$ with ...
3
votes
0answers
218 views

Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
9
votes
2answers
1k views

Is Zitterbewegung an artefact of single-particle theory?

I have seen a number of articles on Zitterbewegung claiming searches for it such as this one: http://arxiv.org/abs/0810.2186. Others such as the so-called ZBW interpretation by Hestenes seemingly ...
5
votes
2answers
458 views

One Loop Higgs Mass Correction

I am attempting to compute the one loop correction to the Higgs mass, which requires the evaluation of a scattering amplitude, namely $$\require{cancel} \mathcal{M} = (-)N_f \int \frac{\mathrm{d}^4 ...
4
votes
1answer
216 views

CP violation from the Electroweak SU(2)$_{weak,flavor}$ by $\int \theta F \wedge F $

Question: Why there is NO Charge-Parity (CP) violation from a potential Theta term in the electroweak SU(2)$_{weak,flavor}$ sector by $\theta_{electroweak} \int F \wedge F$? (ps. an explicit ...
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0answers
63 views

Why Green's function will diverge at the same spacetime point?

In $d+1$ dimensional quantum field theory, the 2-point Green's function will diverge at the same spacetime point when $d\geq1$. When $d=0$, $\phi(t)=q(t)$, that is the case of QM, and 2-point Green's ...
2
votes
1answer
316 views

Weinberg dimension 5 operator

How to prove that the $\Delta L=2,$ dimension=5 Weinberg operator $LLHH$ is the unique operator which violates lepton number by two units, without derivative couplings, etc.??
6
votes
1answer
129 views

Anomalous Dimensions of Gauge Interactions

Peskin and Schroeder mention a few times that the anomalous dimension of a gauge interaction operator is zero. The justification for this is that the charge operator shouldn't get modified under ...
13
votes
2answers
722 views

What does a $SU(2)$ doublet really mean?

What do we really mean when we say that the neutron and proton wavefunctions together form an $SU(2)$ doublet? What is the significance of this? What does this transformation really doing to the ...
4
votes
2answers
156 views

How to conclude that an interaction is attractive from its Fourier transform (momentum space representation)?

Background: In the book by Altland and Simons, Condensed matter field theory, in exercise 4.5.7, one is supposed to use the effective field theory method to integrate out the phonon field in an ...
3
votes
0answers
74 views

1+1D Bosonization on a line segment or a compact ring

I have been informed that 1+1D Bosonization/Fermionization on a line segment or 1+1D Bosonization/Fermionization a compact ring are different - Although I know that Bosonization can rewrite fermions ...
1
vote
0answers
33 views

Is the reduction map completely positive? [duplicate]

I am struggling with proving the complete positivity of a general map ( granted it is CP ). The reduction map is defined as $$ \rho \rightarrow \mathrm{Tr}(\rho)I - \rho $$ It is a trivial job to ...
2
votes
3answers
642 views

Scalar Field Redefinition and Scattering Amplitude

Consider a field redefinition $$ \phi \rightarrow \phi' = \phi+\lambda \phi^2 $$ Find the Feynman rules for this theory and work out the $2\rightarrow 2$ scattering amplitude at tree level (The result ...
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votes
1answer
102 views

Amplitudes involving Goldstone bosons

Does anyone know some theorem or statement about amplitudes involving only Goldstone bosons in theories with spontaneous symmetry breaking in the limit of low energies?
4
votes
0answers
73 views

Is it necessary to use decay width calculated at the same order as the scattering process?

I would like to calculate higher order corrections to a process for which there is an intermediate resonance which subsequently decays into lighter states. I am confused about how to treat the width ...
13
votes
7answers
1k views

Can energy be taken out of the QFT vacuum?

There have been recent questions about the vacuum. In my simplified knowledge the vacuum is like a ground state energy level, and also that there might even exist other lower energy levels than the ...
10
votes
1answer
191 views

Assumptions of the Coleman-Mandula Theorem

In the original paper All Possible Symmetries of the S-Matrix, by S. Coleman and J. Mandula, they prove their famous 'no go' theorem regarding the possible extensions of Poincaré symmetry. The ...
2
votes
1answer
110 views

Materials about S-matrix and S-matrix theory

What is the best book or paper to learn about analytical structures of S-matrix and S-matrix theory? I already know books as The Analytic S-matrix by RJ Eden, PV Landshoff, DI Olive, JC P and Quantum ...
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1answer
238 views

What happens to the wave function after applying the D'Alembert operator?

Is the result of applying the D'Alembert operator on a wave function always zero? Or are there exceptions?
4
votes
1answer
225 views

The BRST construction for YM with or without auxiliary field

I'm learning BRST symmetry for Yang-Mills theory and I see that there are two ways of writing BRST differential. In some books (for example Ryder's and Ramond's textbooks) BRST differential acts as ...
2
votes
2answers
331 views

Angular Momentum Operator in Quantum Field Theory

I'm following along with David Tong's QFT course and am trying to derive the result shown in question 6 on his 2nd problem sheet, but am running into problems when applying it to the free real scalar ...