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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Leptogenesis with singlet neutrinos

(i) The Lagrangian of electroweak model extended with right-chiral singlet neutrinos $N_{iR}$ contains the Yukawa coupling term+ the bare Majorana mass term $$f_{\alpha ...
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272 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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104 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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24 views

vanishing of $\Pi^0$ and non-existence of propagator

We know that if we try to quantize the free electromagnetic field without a gauge fixing term added to the Lagrangian, then one of the conjugate momentum density $\Pi^0$ vanishes. We also find that ...
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217 views

Secondary constraints leads to the value of lagrange multiplier

From Lagrangian I got two primary constraint $\phi_i$ and $\phi$. And my Hamiltonian in presence of the constraints becomes- $$H_p=p\dot q-L+\lambda_i\phi_i+\lambda\phi$$ here the $\lambda_i$ and ...
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43 views

How could the effective electric dipole interaction be derived

In some papers (e.g. Bernreuther equation (1.4), The electric dipole moment of the electron) you can find the electric dipole interaction defined as $$L_I=-\frac i2 ...
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191 views

2 Component Spinor Formalism

In Chapters 34-36 of the Srednicki QFT book, 2 component spinors and their combinations in Dirac and Majorana spinors are carefully constructed. Specifically, in equations 36.14 and 36.15 the ...
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34 views

How does a laser emit light in a coherent state?

Lasers work by stimulated emission of atomic transitions. Stimulated emission produces two photons which, because the particle number is well-defined, projects the field into a Fock state. However, it ...
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19 views

How to calculate explicitly the *external leg correction* diagram

I tried to calculate the Amplitude of the external leg correction of figure 6.1 in Peskin&Schroeder. I focus on the diagram with one incomming charged fermion $f^-$ (with momentum $p'$), then a ...
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25 views

Quantum Fields From Cluster-Decomposition Principle

My question is asking for an explanation of Weinberg's claim that QFT is the only way to satisfy Lorentz invariance and the cluster-decomposition principle. The theory is in his QFT Vol. 1. Below I've ...
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670 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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Does the existence of instantons imply non-trivial cohomology of spacetime?

Gauge theories are considered to live on $G$-principal bundles $P$ over the spacetime $\Sigma$. For convenience, the usual text often either compactify $\Sigma$ or assume it is already compact. An ...
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108 views

Does magnetic monopole violate $U(1)$ gauge symmetry?

Does a magnetic monopole violate $U(1)$ gauge symmetry? In what sense and why? Insofar as I know, there are at least two types of magnetic monopoles. One is the Dirac monopole while the other is the ...
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50 views

Is the elementary charge really a constant of nature? - Accuracy of QED

There are a couple of natural constants; examples are Planck's constant or the Speed of light in vacuum. The elementary Charge is the coupling factor to all Kind of electromagnetic interactions; this ...
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1answer
216 views

What is meant by a local Lagrangian density?

What is meant by a local Lagrangian density? How will a non-local Lagrangian look like? What is the problem that we do not consider such Lagrangian densities?
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23 views

Problem on a computation regarding the annihilation field on Weinberg's book (Ch. 5) [on hold]

This is my first post so sorry in advance is something is not "standard". I have a doubt about a computation that is done in the Weinberg book "The Quantum Theory of Fields". The computation should ...
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20 views

Defining a gauge field for an anisotropic material under strain

I have a Hamiltonian for a system which is somewhat analogous to graphene but with additional degrees of freedom. The Hamiltonian is $H=\sum_q \Psi^\dagger \mathcal{H}\Psi$ where ...
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1answer
93 views

Missing a factor of $\sqrt{\frac{\hbar}{m}}$ in a QFT Practice Problem. Can someone explain why?

I am doing problem 2.3 on page 27 of Quantum Field Theory for the Gifted Amateur. Use eqns 2.46 and 2.62 to show that \begin{equation} \hat{x}_j = \frac{1}{\sqrt{N}} ...
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Some questions on a version of the O'Raifeartaigh model

This form is taken from a talk by Seiberg to which I was listening to, Take the Kahler potential ($K$) and the supersymmetric potential ($W$) as, $K = \vert X\vert ^2 + \vert \phi _1 \vert ^2 + ...
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Getting Slavnov-Taylor identity

Let's have generating functional in path integral form for gauge $SU(n)$ theory with interaction: $$ \tag 1 Z[J] = \int DB D\bar{\Psi}D\Psi D\bar{c}Dc e^{iS}. $$ Here $$ S = S_{YM}(B, \partial B) + ...
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2answers
416 views

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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86 views

Tadpole diagrams in $\phi^3$ theory

In "Quantum Field Theory" by Mark Srednicki, Chapter 9 page 67, after he proves that $\langle 0|\phi(x)|0 \rangle$ vanishes (meaning sum of all connected diagrams with a single source is zero), he ...
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28 views

Physical meaning of the coupling matrix in Fermi golden rule

I am calculating the energy transfer rate using Fermi golden rule where the coupling matrix $M$ is obtained using second order pertubation method. $$ \Gamma_{tran}=\frac{2\pi}{\hslash}|M|^{2}\rho$$ ...
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27 views

Still confused about $ T_i $ generators (Spontaneous Breakdown)

If the Langrangian density is $$L=\frac{1}{2}(\partial_\mu \Phi)\cdot(\partial^\mu \Phi)-V(\Phi \cdot \Phi)$$ where $V(\Phi \cdot \Phi)=\frac{1}{2}\mu^2 \Phi \cdot \Phi + \frac{1}{4}|\lambda|(\Phi ...
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28 views

Running of the Higgs mu term (or: running of individual mass terms in a complicated mass matrix)

I am wondering how to calculate the (one-loop) beta function for an individual mass term that appears in combination with a number of other mass terms in the coefficients of a number of fields. What ...
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Why is photon annihilation associated with the POSITIVE frequency component of the electric field?

I'm reading Glauber's paper "The quantum theory of optical coherence". In his work he does not introduce the annihilation and creation operators, but he refers instead to the positive and negative ...
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QFT Perturbative analysis of multiple atom-level quantum computers close to each other

Following up on this question, I'm wondering about electromagnetic interactions perturbation expansions close to a "black-box" quantum computer and modularity of Feynman diagrams in general. Let me ...
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88 views

Invariance of the QED Lagrangian under charge conjugation

Is it true that the QED Lagrangian $$\mathcal{L} = \bar{\psi}(i\gamma^\mu D_\mu-m) \psi $$ is invariant under charge conjugation? $$\begin{align} \psi &\mapsto -i(\gamma^0 \gamma^2 \psi)^T\\ ...
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2answers
295 views

Moving between degenerate vacua?

In spontaneous symmetry breaking, moving round the circular valley of Mexican hat potential doesn’t cost energy. These angular excitations are called Goldstone bosons. But doesn't the angular ...
5
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1answer
223 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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3answers
159 views

Is Parity really violated? (Even though neutrinos are massive)

The weak force couples only to left-chiral fields, which is expressed mathematically by a chiral projection operator $P_L = \frac{1-\gamma_5}{2}$ in the corresponding coupling terms in the Lagrangian. ...
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1answer
23 views

Positronium energy level in QED

I'd like to know if it is possible to compute positronium mass and lifetime from a QED approach. I'm searching for some literature on how to treat resonances in QED (or general QFT) ; most of the ...
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1answer
82 views

difference between instantons and sphalerons

What is the difference between instantons and sphalerons? If they are different, how do they violate baryon and lepton number in the standard electroweak theory?
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59 views

Why string theorist use the following result? [duplicate]

$1+2+3.......$so on $ = -1/12.$ I have seen a few proofs of this result. And I hope most of you are familiar with them. Why string theorist use this ambiguous result in string theory, when assigning ...
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3answers
163 views

Are vacuum fluctuations really happening all the time?

In popular physics articles and even some physics classes I've been to, the vacuum of space is described as being constantly full of quantum fluctuations. Supposedly, all sorts of ...
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1answer
79 views

Why does this condition ensure that the residue of the propagator is 1?

The corrected propagator is given by $$\Delta'(q)=\frac{1}{q^2+m^2-\Pi^*(q^2)-i\epsilon}$$ ($\Pi^*$ is the sum of all irreducible one-particle amplitudes) I get that the residue of the original ...
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1answer
72 views

Why does the electric field escape a black hole?

An (unlikely) charged black hole can be described with the mass, angular momentum, charge and the thermal radiation. The reasoning behind the thermal radiation rests on the particle creation outside ...
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2answers
168 views

What is the essence of the Unruh-effect?

The essence of the Unruh effect is basically that coordinate-transformations lead to different excitations/occupation numbers of the quantum fields. Is that statement correct? So in QFT, while an ...
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73 views

Why instantons can not cause confinement in 4d?

I am reading Aspects of Symmetry by Sidney Coleman. More specifically I am trying to learn about instantons, and I would like some clarifications. In chapter 7, section 4. he derives confinement in ...
2
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1answer
76 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
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35 views

What is the essence of the renormalization flow? [closed]

Recently I started learning QFT and I am trying to understand the renormalization group (RG), however I have some difficulties. Is the whole concept just based on tracing out certain (irrelevant) ...
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1answer
27 views

Lagrangian density with explicit $x_\mu$ dependence

In the Quantum Field Theory book, by Ryder, he says that a Lagrangian density of a field can also be an explicit function of $x_\mu$ if the field interacts with external sources. Can someone give an ...
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26 views

What are the simplest quantum 1D spin chain models which aren't integrable?

What are the simplest quantum 1D spin chain models which aren't integrable? Are there any generic criteria for telling whether or not a given quantum 1D spin chain model is integrable?
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Is an electron technically a set of two particles?

The electron - described as a four-spinor in the Dirac equation - transforms according to the $(1/2,0)\oplus(0,1/2)$ representation of the Lorentz group, so it is actually a direct sum of a left- and ...
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1answer
956 views

Is a photon technically a set of two particles?

When looking at the classification of massless particles, one finds that there is the (half-integer) quantum number "helicity" $h$. For every possible $h$ there is a certain particle kind. In the case ...
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Is frequency quantized in the black body spectrum?

I'm aware that there're some questions posted here with respect to this subject on this site, but I still want to make sure, is frequency quantized? Do very fine discontinuities exist in a continuous ...
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1answer
78 views

What is the relation between a basis transformation and an induced transformation $\psi(\Lambda^{-1} p)$ on the wave function? [closed]

I'm having trouble understanding why is $\psi(\Lambda^{-1}p')$ the correct wave function in the Lorentz transformed frame $p' = \Lambda p$. Suppose the state in frame $O$ is given by $$ ...
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1answer
30 views

Fractional exponent in a scalar quantum field: Is energy and momentum conserved in this case?

Assuming that I would have the following term in the Lagrangian for a scalar boson field $$L=\int d^4x g (\phi^{2-p} \phi^{\dagger 2+p}+\phi^{\dagger 2-p} \phi^{2+p}))$$ with a fractional number $p$. ...
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20 views

How to understand the Bose glass phase has infinite superfluid susceptibility?

The Bose glass phase is characterized by a gapless excitation spectrum, exponential decay of superfluid correlations, finite compressibility and infinite superfluid susceptibility. The disordered ...
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29 views