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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What is the physical interpretation of the automorphism on bounded operators induced by an S matrix?

In a QFT, the S-matrix $S$ is a unitary operator, that fixes the vacuum and commutes with the unitary operators implementing the action of the Poincare group on an appropriate Hilbert space $H$. ...
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40 views

What is the difference between Fermi golden rule and Wigner-Weisskopf theory?

What is the difference between Fermi golden rule and Wigner-Weisskopf theory? They both deal with the spontaneous emission process. So what is the difference? As far as I know, the fermi golden rule ...
3
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2answers
55 views

Why do the $u$ and $d$ quark not have an associated quantum number?

All the other quarks ($c$,$s$,$b$ and $t$) have quantum numbers of charmness, strangeness, bottomness and topness that are conserved in strong interactions. This allows, among other things, flavour ...
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3answers
107 views

Does Peskin & Schroeder Eq. (4.26), $U(t_1,t_2)U(t_2,t_3) = U(t_1,t_3)$ imply $[H_0,H_{int}] = 0$?

Peskin & Schroeder equation (4.17) define the operator, \begin{equation} U(t,t_{0})~=~e^{i(t-t_{0})H_{0}}e^{-i(t-t_{0})H} \tag{4.17} \end{equation} where $$H~=~H_0+H_{\text{int}}\tag{4.12}$$ is ...
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1answer
30 views

Dirac Current Spectral Representation

I'm reading Strocchi's book on The Non-Perturbative Foundations of Quantum Field Theory. In the chapter concerning point-splitting regularization, where the free Dirac current is defined as follows ...
2
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124 views

Perturbation theory : quadratic external field

I'm trying to derive the explicit form of S-matrix of an interaction Hamiltonian $$H' = \frac{1}{2} \lambda \left[ \int d^3 x \rho({\vec x}) \phi({\vec x}, t)\right]^2\tag{1}$$ Even though the ...
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1answer
135 views

Path integral in quantum mechanics

I am confused by the derivation in Srednicki QFT's chapter 6 from (6.8) to (6.9). In (6.8), we have $$<q'',t''|q',t'>~=~\int DqDp \exp[i\int_{t'}^{t''}dt(p\dot{q}-H(p,q))],\tag{6.8}$$ and ...
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20 views

Do cosmic strings or global monopoles interact with magnetic field?

Does anyone know any phenomenon that shows the interaction between cosmic strings or global monopoles with magnetic field? I looked for that in Vilenkin and Shellard's book but, as I'm not a ...
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2answers
95 views

How to tell the order of a Feynman diagram?

How can we know the order of a Feynman diagram just from the pictorial representation? Is it the number of vertices divided by 2? For example, I know that electnro-positron annihilaiton is first ...
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75 views

Anderson-Higgs mechanism for the (non-relativistic) $U(1)$ gauge theory under the unitarity gauge

On Page 138, Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons by Xiaogang Wen, when he demonstrates the Anderson-Higgs mechanism for the $U(1)$ ...
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1answer
58 views

Independent Phases in Gauge Theory

Excuse my naivety. When we postulate a local gauge invariance we say that we allow the overall phase of the field variables $\psi(x)$ can be changed and that this overall phase can vary from point to ...
3
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1answer
43 views

Why is the photoelectric absorption coefficient finite at the threshold frequency?

I mean the photoelectric effect of the hydrogen atom. It is weird. By the Fermi golden rule, the transition or absorption rate is proportional to the density of the final states. At threshold, the ...
3
votes
1answer
105 views

Spin operator: tricky proof using gamma matrices

I have not dealt with the gamma matrices extensively so I am having a bit of trouble here. Basically I want to show that the spin operator defined by $$ \mathbf{\hat{S}} = \frac{1}{2}\gamma^5 ...
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26 views

dagger operator in spinor representation

I just have trouble understanding how hermitian conjugation is acting like this in the following example (dot represents right-handed Weyl field, undot represents left-handed Weyl field). For ...
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1answer
63 views

Can one apply the Hubbard-Stratonovich transformation to the exponential of the Laplacian?

Is there a generalization of the Hubbard-Stratonovich transformation that transforms the exponential of the Laplacian into a Gaussian integral? Or can anyone suggest me how I can find the ...
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2answers
57 views

What does the “UV” in “UV completion” stand for? [closed]

What does the "UV" in "UV completion" stand for? Also, I'm not sure which tags I should tag this question with.
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1answer
52 views

Hermitian Adjoint of Spinor

Say we have a four component spinor $\psi$: $$ \psi=\begin{pmatrix}\psi_L\\\psi_R\end{pmatrix} $$ Is the Hermitian adjoint of this: $$ \psi^\dagger =\begin{pmatrix}\psi_L^\dagger ...
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60 views

Why is the electric field operator normalized by a volume?

I came across the following definition of the electric field operator: But I am not sure what this $V$, the "volume of a box", is about. It seems to enter the discussion in order to have standing ...
4
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1answer
139 views

Lorentz Algebra Representation and QFT

I just have a trouble making a full analogy between Lorentz Algebra Representation in Quantum Field Theory (QFT) and SU(2) representation in Quantum Mechanics (QM). To make my point, I will write few ...
4
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2answers
82 views

Destroying currents in superconducting rings by vortex tunneling

Consider a superconducting metal ring in which there is a persisting current $I$. I am interested in the failure of this current to remain "persisting" in the ring, although this will occur at ...
3
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1answer
67 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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31 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
116 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
40 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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26 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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24 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
47 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: $$iG_F(x,x')=\langle0\lvert T[\phi(x)\phi(x')]\rvert0\rangle \tag{1}$$ ...
5
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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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37 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
98 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
votes
1answer
76 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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40 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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1answer
90 views

Hidden Weyl symmetry & fixed metric lead to simplified correlators

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 $$ ...
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1answer
62 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 ...
0
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1answer
63 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. ...
2
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1answer
58 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
59 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
30 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 ...
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1answer
167 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
34 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 $b_{x}$, ...
0
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2answers
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}) = ...
3
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3answers
97 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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34 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
67 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
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 ...
4
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0answers
66 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
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
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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0answers
34 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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21 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 ...