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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72 views

Why do electrons in a superconductor lack energy to produce “massive” photons

My two questions are based around looking for a good, simple (if possible) explanation of the Cooper pair effect in superconductors. I follow the idea that, in intuitive terms, "a Cooper Pair" ...
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40 views

Feynman Parametrization in muon magnetic moment

I am calculating the muon magnetic moment due to Electroweak interactions in one loop diagrams involving $W$ bosons. While referring a particular research article by John S. Curiale, titled Weak ...
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2answers
124 views

Strangeness of QFT [closed]

In quantum field theory, the particle-wave duality is resolved by assuming that a field can collapse to some quantum value. Suppose you are observing a distant star through a small aperture that ...
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0answers
63 views

Argument of E. Fradkin on the mean-field theory of spin liquids

I have read the chapter 8 of Field Theory of Condensed Matter Physics (2ed.) by E. Fradkin a couple of times, but I still confused by his argument at some points. I hope you can help me with that. ...
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0answers
44 views

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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26 views

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): ...
2
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1answer
52 views

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: $$iG_F(x,x')=\langle0\lvert T[\phi(x)\phi(x')]\rvert0\rangle \tag{1}$$ ...
4
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1answer
106 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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48 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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1answer
149 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 ...
2
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1answer
105 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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43 views

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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2answers
123 views

Simplifying effect of a hidden Weyl symmetry in a QFT on curved spacetime

We consider AdS$_{d+1}$ in Poincaré coordinates: $$ ds^2=\frac{1}{z^2}\left(-dt^2+dz^2+dx_{d-1}^2\right), $$ where we set the AdS radius to unity. We study a scalar in this background with action $$ ...
2
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1answer
78 views

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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1answer
71 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. ...
3
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1answer
65 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 ...
3
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1answer
75 views

Pole Mass vs. Running Mass vs. Other Running Parameters

Unless I'm mistaken, physical masses that one goes out an measures in experiments corresponding to the location of poles in the propagator and such pole masses are independent of the energy scale of ...
2
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0answers
39 views

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 ...
7
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1answer
170 views

Cluster decomposition in string theory

Do amplitudes and correlation functions in string theory satisfy the cluster decomposition principle? Note added: Even without local observables such as correlation functions, one can define the ...
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0answers
43 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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2answers
61 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}) = ...
3
votes
3answers
112 views

Fourier Transforms Related to Green's Functions

I'm reading a text on field theory where there are a number of assertions made about Fourier transforms that I'm finding confusing. For example, let $G^R = -i \theta(t - t')e^{-i \omega_0 (t - t')}$. ...
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41 views

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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2answers
87 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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1answer
59 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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70 views

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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1answer
108 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
42 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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0answers
40 views

Dependence of finite part of loop integral on regularization

Recently I've calculated some process in which arise triangle loop with running two $W$ bosons and one massless fermion. The expression for integral is following: $$ I_{\alpha \beta}(r, q) = \int ...
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0answers
27 views

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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0answers
58 views

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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0answers
43 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 ...
2
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1answer
68 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 ...
4
votes
1answer
67 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
68 views

Virtual particles and the scaling effect on valence quarks

Inside a proton there are 3 valance quarks. In addition, there is constant creation and annihilation of gluon, quarks and anti-quarks. The number of virtual particles we observe depends on how ...
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30 views

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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1answer
39 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) ...
4
votes
1answer
97 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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0answers
86 views

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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1answer
85 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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0answers
91 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 ...
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0answers
61 views

Why do we use Fourier transforms in QFT? [duplicate]

I ask this question, as someone has recently asked me this and I'm not sure I gave them a satisfactory/correct answer. I explained that in QFT we describe particles (and there interactions) in terms ...
2
votes
2answers
91 views

Identify for $f(\infty)+f(-\infty)$ in quantum field theory [duplicate]

In Matthew Schwartz's textbook, Quantum Field Theory and the Standard Model, equation 14.68 on page 266 says the following: ...
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1answer
25 views

Translational versus dilatational zero modes?

Why are the zero modes of the SU(2) Yang Mills instanton referred to as translational or dilatational zero modes? Is this standard terminology?
4
votes
1answer
90 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} ...
3
votes
2answers
114 views

How to count the number of modes/polarizations of a Gaussian field theory?

A Gaussian (free) field theory is described by a quadratic action of the field, e.g. $S=\int\psi^\dagger K\psi$ (or $S=\frac{1}{2}\int\phi^\intercal K\phi$ for real fields). Usually one just need to ...
2
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1answer
159 views

effective field theory of the projective semion model

The "projective semion" model was considered in http://arxiv.org/abs/1403.6491 (page 2). It is a symmetry enriched topological (SET) phase. There is one non-trivial anyon, a semion $s$ which induces a ...
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2answers
115 views

Viability of a Fayet Iliopoulos term in the MSSM

Why is a Fayet-Iliopoulos term $-kD$ irrelevant or subdominant in the in the MSSM (Minimal Susy Standard Model)? According to Martin (A Supersymmetry Primer, p.70) it's because squarks and sleptons ...
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2answers
90 views

Why does the Higgs field have less energy when it's non-zero than when it's zero?

Why does the Higgs field have less energy when it's non-zero than when it's zero? There are references to this question on the site, but they are too heavy going for me for a while yet. Anybody want ...
4
votes
1answer
77 views

Is there a 2D manifold on which the Dirac equation has a zero mode?

The two-dimensional (2D) Dirac equation $(\sigma_1iD_1+\sigma_2 iD_2)\psi=E\psi$ admits zero mode ($E=0$) solutions on a non-trivial gauge background, such as the zero mode at the core of a U(1) gauge ...