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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Intrinsic CPT phase

Under charge conjugation C, spatial inversion P and time reversal T transformations, there are possible intrinsic phases (more for this on Chapter 9, The Quantum Theory of Field v1 by S. Weinberg): ...
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Fujikawa's method for 2+1-dimensional parity anomaly?

Fujikawa's chiral rotation method is applied to calculate 3+1 dimensional chiral anomaly in many textbooks, but is there any counterpart of that method in deriving 2+1 dimensional parity anomaly, i.e. ...
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Physical Interpretation for Schwinger and Hadamard functions

In quantum field theory one usually calculates the Feynman propagator defined as the time ordered product of (scalar) fields: $$iG_F(x,x')=\langle0\lvert T[\phi(x)\phi(x')]\rvert0\rangle \tag{1}$$ ...
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103 views

What is the *quantum* of a field?

The particles of nature are the quanta of relativistic quantum fields, from what I've understood. But what does this mean physically? Is the electron the quantum of an electron field? In what sense, ...
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101 views

Quantizing highly nonlinear field-theories?

I'm wondering how to go about quantizing a classical field theory which looks nothing like a free field theory plus a perturbation term. Suppose for concreteness I have the classical hamiltonian $ ...
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74 views

Proper way to quantize the string in the light-cone gauge

In many books like Polchinski and Green-Schwarz-Witten the light cone quantization is carried out in a fast way. They just use the virasoro constraint in the light-cone gauge to get the ligh-cone ...
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246 views

Branch cuts in two-point function

The propagator of a QFT is known to have a branch cut as a function of the (complex) external momentum. The branch point (as done by, say, Peskin & Schroeder in eqn.7.19 section 7.1) is ...
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34 views

Anomaly and Weyl spinors

I try to better understand anomalies in QFT and I've got a question concerning derivation of axial anomaly in Terning's lectures (page 12) Consider a theory of Weyl fermions coupled to a gauge field ...
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198 views

A question about the energy of turning on and off interaction adiabatically in QFT

I read a saying as follows: In a theory with no particles which decay and no bound states, the turning on and off of the interactions merely serves to limit the effective range of forces. In this ...
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80 views

Viability of a Fayet Iliopoulos term in the MSSM

Why is a Fayet Iliopoulos term $-kD$ in the MSSM (Minimal Susy Standard Model) not relevant (or subdominant to an F-term)? According to Martin (A Supersymmetry Primer, p.70) it's because squarks and ...
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119 views

Massless boson in 2D and its (retarded) propagator

I have the retarded propagator for a free scalar field in 1+1 dimensions. Inside the light cone, this looks like $J_0(m \sqrt(t^2-x^2))$, J being a Bessel function. When I take the massless limit, ...
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93 views

We Don't NEED Quantum Gravity because Gravity isn't Even A Force! [duplicate]

Now, I understand the motivation for quantum gravity. I honestly want to work on a theory myself. However, gravity, according to General Relativity, is not a fundamental force of nature. To me, it's ...
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What to do when finite counterterms are undetermined?

Suppose I have some theory of "new physics" which involves interaction of some gauge boson with Standard model. For this theory I have some loop-mediated process with this new gauge boson whose matrix ...
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Gauge symmetry is not a symmetry?

I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
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Meaning of “vacuum state”?

I just learned about $|0\rangle$ and siblings $|0_\gamma\rangle$ and $|0_\infty\rangle$ while studying coherent and squeezed states in a QM class, and I have a question about the meaning of ...
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790 views

Kramers-Kronig relations for the electron Self-Energy Σ

I'm currently studying an article by Maslov, in particular the first section about higher corrections to Fermi-liquid behavior of interacting electron systems. Unfortunately, I've hit a snag when ...
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284 views

Determinant for a coupled fluctuation Lagrangian

Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
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57 views

What is the phase of a gauge coupling?

We typically take gauge couplings to be real and positive. Why do we impose these two conditions? I assume this is a requirement because gauge theories without positive couplings are unphysical or is ...
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62 views

Space-time translations and Propagator

Let us assume to have the following scalar field theory $$ {\cal A}=\int d^4x\left[\frac{1}{2}(\partial\phi)^2-\frac{\lambda}{4}\phi^4\right] $$ where I used a quartic potential to fix the ideas. ...
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33 views

Low-energy “effective measure” from superstrings?

There is obviously a gap in my knowledge of the origin of effective actions in string theory. As far as I understand it, the strategy is straightforward (at least in principle): Write down the ...
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57 views

Schrodinger field and klein gordon field

In the usual Fourier expansion of schrodinger fields \begin{align} \Psi(\vec{x}) = \frac{1}{(2\pi)^{\frac{3}{2}}} \int d^3 k \hat{a}_k e^{-i (wt-\vec{k}\cdot \vec{x})}, \quad \Psi^{*}(\vec{x}) = ...
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What physical effects cause materialization of a system of particles for a short time?

It is well-known from physics that a photon with enough energy creates a pair of particles: one electron and one positron. This pair of particles can only exist for a short time. This process is ...
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33 views

commutation relations for operators in projected subspaces

I am looking for a consistent re-definition of commutators for certain operators when I work in a projected subspace. Basically, I have a spin defined in terms of 4 Majorana operators $b_{x}$, ...
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Path integrals and Weyl ordering in Peskin and Schroeder [duplicate]

On pages 280-281 of "An Introduction to Quantum Field Theory" by Peskin and Schroeder, the authors discuss the path integral formulation for a general quantum system and briefly mention Weyl ordering. ...
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388 views

Teach me Wick's theorem the honest way

Generally speaking the average guy marginally acquainted with quantum field theory or advanced combinatorics describes Wick's theorem as some sort of correspondence between higher order differential ...
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128 views

Group theoretic way to find charges after SSB

I was wondering what is the group theoretic way to find the resulting charges of matter fields after a scalar field is given a vev. In the case of the EW symmetry breaking, one can directly read the ...
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A question on intermediate step in deriving gravitational anomaly by Fujikawa's method

In Fujikawa's 'Path integrals and Quantum Anomalies', Eq.(10.26) in the derivation of gravitational anomaly in Chapter 10.1 is puzzling for me. ...
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1answer
56 views

Product of deltas in kinetic second quantization hamiltonian

I am trying to derive the result for a kinetic hamiltonian in second quantization in term of the fields, that is: $\hat{H} = \int - \Psi^\dagger (r) \frac{\hbar^2\hat{\nabla}^2}{2m} \Psi(r)$ I start ...
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64 views

Gauge transformation of Lagrangian

Suppose I have a Lagrangian density $\mathcal{L}(\phi^\mu,\sigma)$ depending on vector fields $\phi^\mu$ and their derivatives and a scalar field $\sigma$ and its derivatives. If I make a gauge ...
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227 views

A question about causality and Quantum Field Theory from improper Lorentz transformation

Related post Causality and Quantum Field Theory In Peskin and Schroeder's QFT p28, the authors tried to show causality is preserved in scalar field theory. Consider commutator $$ [ \phi(x), \phi(y) ...
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1answer
100 views

Is there a mistake in a QFT textbook?

I tried to calculate one of the problems in the textbook Gauge Theory of Elementary Particle Physics by Ta-Pei Cheng and Ling-Fong Li. On page 248 you can find the following calculation of a loop ...
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1answer
119 views

Fock representation of a electromagnetic wave

Suppose an arbitrary classical (electromagnetic) wave package $E(x)$. What is its Fock space representation? I.e. I am looking for a state $| \psi \rangle$ such that $\langle \psi | \hat E(x) | \psi ...
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338 views

Speed of light and virtual particles

After becoming extremely bored while studying for an Afrikaans exam, I started thinking about virtual particles. So, can light (photons) interact with virtual particles (even though they only exist ...
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86 views

Why is tree-level interaction between neutral scalar and photons non-renormalizable?

I've read that the decay of a neutral scalar particle into two photons, i.e., $$ S(p+q) \to \gamma(p) + \gamma(q) $$ can't happen via tree diagrams and instead is caused by loop diagrams (such as a ...
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731 views

Analytic continuation of imaginary time Greens function in the time domain

Consider the imaginary time Greens function of a fermion field $\Psi(x,τ)$ at zero temperature $$ G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle $$ ...
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1answer
74 views

Why does this proof show the gluon propagator comes from the first two terms?

I am reading the book "QCD: Renormalization for the Practitioner" and i am having trouble understanding something. In page 70 the gluon propagator is written as follows $$\begin{multline} ...
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Does a momentum-independent interaction not renormalize mass?

I recently had to calculate the effective mass to second-order in a momentum-independent interaction in a Fermi liquid, and I found that it was the same as the bare mass. What's more, the first-order ...
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Equivalence of delta functions when calculating decay rate [closed]

$\newcommand{\bs}{\boldsymbol}$ Hello, I'm currently working through the lecture notes of my Theoretical Particle Physics course, and there, we are calculating the decay rate of the following process ...
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40 views

Form of the S matrix for interacting scalar field [closed]

The solution for the equation $ S^{-1} c_k^{in} S = c_k^{in} + f_ k $ is S= $ exp(f_k^{*}c_k^{in} - f_kc_k^{in*})$. Here $c_k^{in}$ is an operator and $f_k$ is a c number. This is the equation for ...
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64 views

Vacuum has zero spin in Dirac theory

I have troubles trying to prove a statement made by Peskin-Schroeder in page 61, section 3.5 where he says that the "spin" operator $J_z$ given by the non numbered equation $$ J_z= \int d^3 x ...
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698 views

Could this model have soliton solutions?

We consider a theory described by the Lagrangian, $$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$ The corresponding field equations are, ...
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758 views

Does anyone take the Wightman axioms seriously?

Does anyone take the Wightman axioms seriously? Mainly with respect to quantum gravity or gauge theores, abelian or non-abelian? Anyone doing any research on axiomatization of QFTs in some way?
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Quantum to classical mapping: quantum criticality and path integral Monte Carlo

I'm trying to understand the connections between quantum models in d dimensions and classical models in (d+1) dimensions within two, possibly related, contexts: (i) in path integral monte carlo, the ...
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1answer
60 views

Origin of the quark condensate VEV

Consider the QCD lagrangian : $$L_{QCD}=-\frac{1}{4}G^a_{\mu\nu}G^{a\mu\nu}+\sum\bar{\psi}_q(i\not{D}-m_q)\psi_q$$ Textbooks explain that this lagrangian is spontaneously broken by the VEV of quark ...
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1answer
44 views

Using the optical theorem to calculate the imaginary part of a loop diagram

I'm trying to calculate the imaginary part of this diagram in $\phi^4$ theory, using the optical theorem, and I'm having trouble. All of the examples I can find use the theorem to relate the ...
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Calculating imaginary part of a loop diagram using cutting rules for phi^4 theory [closed]

I'm trying to calculate the imaginary part of this diagram in $\phi^4$ theory, using the optical theorem, and I'm having trouble. The cutting rules seem to suggest that this diagram is equal to ...
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is there any molecular transition which emits a photon in certain direction

i know molecules having magnetic moment would be aligned in certain direction but do they emit photon in any certain direction when excited? are there any molecules which would emit photon in tthe ...
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31 views

Time evolution of generalized angular momentum operator

We define this operator : $$M^{\mu\nu} = \int d^3x~(x^{\mu}T^{0\nu} - x^{\nu}T^{0\mu})$$ where $T_{\mu\nu}$ is the energy momentum tensor (see e.g. Energy momentum tensor from Noether's theorem) ...
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1answer
239 views

Calculating $\mathrm{Tr}[\log \Delta_F]$

I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this question), which looks like $$ \widetilde\Delta_F(p) = ...
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68 views

Anomaly for Majorana fermion?

In 4-spacetime dimension, is there U(1) gauge field chiral anomaly associated with Majorana fermion (or I am not sure if it is equivalent, majorana representation)? Besides, I have read from several ...