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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The relation between anomalous dimensions and renormalization constants

I am trying to understand the general strategy and technical details of calculating $\beta$-function at higher orders. $\beta$-function is the anomalous dimension of the coupling constant and there is ...
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20 views

Why do quasi-free states satisfy the positivity condition?

In LQFT, a state, $\omega$, is a linear map $\omega:A=:CCR({\cal{S}},\Omega)\rightarrow \mathbb{C}$ satisfying: $\omega(aa^{*})\geq 0$ for all $a\in A$. $\omega(I)=1$ where $I$ denotes the identity ...
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2answers
237 views

Doppler effect of matter waves

We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object. We also know the the concept of particle-wave ...
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12 views

Polarized Moller scattering cross section

When doing a computation of scattering cross sections of particles with spin, one usually averages over the initial spins and sums over the final ones. I'm a bit puzzled as to how to do the ...
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1answer
36 views

Why we have to sum in all final states of hadrons?

Correct if I am wrong. In deep inelastic scattering have to sum in all final sates hadrons because we do not want to detect the hadrons. All we want to detect is the electron. Am I right?
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69 views

Why do we learn only two computations, cross sections and decay rates, in such a fundamental theory as QFT?

When I learned Newtonian mechanics I found a vast variety of computations that I could do and that was so interesting. And it was so when I learned Maxwell theory. When I started learning QFT I hoped ...
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1answer
111 views

Unruh radiation and conservation of energy

Consider the Minkowski spacetime filled by some fields in their Minkowskian vaccum state. Now consider a Rindler observer carrying with him, say, one liter of water. According to Unruh formula, the ...
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1answer
22 views

Is the time ordering in Dyson series either 1 or -1?

Because I think to make it a unitary operator, the norm of the unitary operator should be one. But I did not see any claim about the value of time ordering in Dyson series.
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1answer
589 views

Eikonal approximation in QFT

Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
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26 views

Heisenberg uncertainity principle is valid in the case of QFT? [duplicate]

The Heisenberg uncertainty principle is valid (or taken into account) in the case of QFT?
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29 views

How do (special) groups such as U(1) and SU(2) do represent the electromagnetic and weak forces? [on hold]

I don't see how groups, such as the circle group somehow representing electromagnetism, represent the fundamental forces. Where is this connection between maths and theoretical physics? Also, as a ...
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17 views

Can charged scalar have non zero vev?

In Higgs-Kibble mechanism, if we consider a SU[2]_L doublet of complex scalar fields, then one of them is charged and the other neutral. Why does the neutral field acquire vev and not the charged one? ...
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1answer
125 views

What are skeleton diagrams and what is their use in qft and many-body physics?

How does one construct skeleton diagrams from specific Feynman diagrams (e.g. for the electronic Green function in QED and in many-body gases, for the polarization function, for the vertex function, ...
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1answer
511 views
2
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1answer
135 views

S-matrix in Weinberg QFT

I'm a bit confused by Weinberg's discussion of scattering. He defined the in and out states $|\Psi^{\pm}_\alpha\rangle$ with particle content $\alpha$ as states that transform under the Poincare group ...
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2answers
53 views

bare Phonon and Symmetry Breaking

In condensed matter physics, the phonon is considered as a quasiparticle which is a result of the quantization of lattice vibrations. In many textbooks on solid state physics, it can be done if we ...
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1answer
300 views

Simple QFT simulation - how to do it

I would like to write a simple QFT simulation for a free scalar field with a cubic interaction term. However, I got stuck a bit. I will try to describe what I think I understand. I want to have a ...
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1answer
62 views

Is there one wavefunction per field? [on hold]

Is the big picture of quantum field theory that: There are fields (EM, electron, Higgs, gravity, etc.) A field can be described by a wavefunction indicating the probability density of 1 or more ...
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1answer
237 views

Does it make sense to speak of amplitudes of finite closed boundaries in QFT?

A example of amplitude in Relativistic Quantum Mechanics or specifically in QFT is the amplitude of a field configuration on a space-like hyper-surface of space-time to "lead" to another field ...
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91 views

Photons are self-conjugate but neutrinos may or may not: why is that?

Caution: This may be a very naive question but I find it confusing. Moreover, I believe this question is based on potential misconception. I would like it to be clarified. Although the neutrinos are ...
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3answers
175 views

Complex scalar field theory

For the complex scalar field theory $$L = -\partial_{\mu}\phi^{*}\partial_{\mu}\phi - m^{2}\phi^{*}\phi + J\phi^{*}+J^{*}\phi,$$ Why is there no factor of 1/2 in the lagrangian like in the real ...
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20 views

What is the most essential theoritical constrains should be imposed on arbitrary potential's parameters?

I'm little confused about the unitarity and perturbativity constrains which imposed on a potential's parameters, like 2HD potential. Look for example: [arXiv:1507.03618v3 [hep-ph]] First, I'd like to ...
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68 views

QFT Weinberg scattering thoery [on hold]

I have a question about beginning of chapter 3 (scattering) of QFT.vol.1 by Weinberg I think (am I wrong?) $\Psi_\alpha$ means a collection of particles each with a definite $p^\mu$ specially $p^0$ ...
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42 views

Higgs mechanism in quantum GLSM

My question is regarding the following Gauged Linear Sigma Model (GLSM) in two dimensions. $$\tag{1} S=\int d^2x\Big(-D_{\mu}\overline{\phi} D^{\mu}\phi +\frac{D^2}{2e'^2} +D(|\phi|^2-r)\Big).$$ ...
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1answer
387 views

Momentum Space Renormalization of $\phi ^6 $ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d $ for the energy functional: $$ f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2 $$ where $\ d$ is the dimension ...
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33 views

Non-abelian current commutators

There many articles, in which non-abelian current commutators are computed. The general result is that quantum corrections lead to additional term in commutator $$[J^a_\mu (x), J^b_\nu (y)] \delta ...
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Sudakov double logarithm

I have calculated a few NLO corrections in QED and in the final result the Sudakov double logarithms have always canceled. So I thought that they have no physical meaning. On the other hand I have ...
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189 views

Classical field limit of the electron quantum field

In order to recover classical electromagnetic fields from the quantum electromagnetic field, we consider coherent states of the form $$\exp \left(\int d\vec{r}\, \vec{A}(\vec{r}) ...
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1answer
186 views

Explaining causal completion axiom in Haag-Kastler axioms?

There are several variants of the Haag-Kastler axioms for algebraic quantum field theory. Usually one associates an algebra $\mathcal{A}(O)$ to each open region $O$ of spacetime. An often-suggested ...
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3answers
2k views

Hypercharge for $U(1)$ in $SU(2)\times U(1)$ model

I understand that the fundamental representation of $U(1)$ amounts to a multiplication by a phase factor, e.g. EM. I thought that when it is extended to higher dimensional representations, it would ...
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1answer
3k views

Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view: Anomalies are due to the fact that quantum field ...
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0answers
49 views

Connexion of S matrix and path integral [closed]

I have been studing the path integral formalism but all I am finding is how to calculate time ordering product. How can we connect it with the S-matrix in the canonical formalism?
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1answer
102 views

Confusion in understanding of quantum fluctuations and vacuum energy

I'm having a bit of trouble understanding what exactly is meant by a quantum fluctuation of a quantum field and its relation to the vacuum energy attributed to such a field. Is the point, that due ...
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1answer
115 views

Quantum field theory with constraint: energy-momentum conservation?

Suppose I have a 2-form field $B$ and a Lagrange multiplier field $\lambda$, then the Lagrangian $S = \int (B \wedge \delta B + \lambda \delta B \wedge \delta B)$ with a Lie derivative operator ...
3
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1answer
171 views

Singlet neutrinos decaying to Higgs bosons during leptogenesis

(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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Do the broken symmetry functions of a Mexican hat potential form a smooth function throughout space?

When the symmetry of a Mexican hat potential is spontaneously broken, the new zero potential comes to lie on one of the points on the rim of the hat (the collections of potentials with zero as value). ...
3
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1answer
55 views

Propagator from Path integral

In class we have proved something like: $$ \frac{\partial^2 Z(J,\bar{J})}{\partial J(x) \partial \bar{J}(x')}\frac{1}{Z}|_{J=\bar{J}=0}=\Delta(x-x').$$ That by introducing source terms to path ...
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1answer
57 views

Vacuum expectation value in presence of a source

If a vacuum is translationally invariant i.e., $P^\mu|0\rangle=0$ or $e^{(\pm ip\cdot x)}|0\rangle=0$, we can express the the vacuum expectation value of a field as $\langle 0|\phi(x)|0\rangle$ as ...
3
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1answer
26 views

About series expansion of effective potential and its justification

The books on quantum field theory often uses an expansion of the effective action $\Gamma[\phi_c]$ in terms of $\phi_{cl}$ and its derivatives given by $$ \Gamma[\phi_c]=\int ...
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33 views

Klein Gordon, Dirac, Proca [closed]

How do we know these equations : Klein-Gordon, Dirac, Proca is for spin 0, spin 1/2 , spin 1? How did people find Klein Gordon doesn't work for spin 1/2?
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1answer
49 views

Physical interpretations of the generating functions $Z[J]$ and $W[J]$ (or $E[J]$)

In quantum field theory, the generator of all Green's functions $Z[J]$ and that of the connected Green's functions $E[J]$ are related as $$Z[J]=\exp[-iE[J]]=\int D\phi\exp[i\int ...
6
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1answer
271 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 $ ...
7
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1answer
182 views

Wilsonian vs 1PI

As a follow up to Difference between 1PI effective action and Wilsonian effective action, where can I find pedagogical material that highlights the similarities and differences between the 1PI and ...
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0answers
18 views

Hankel transformation of Yukawa potential [closed]

This is a Hankel transformation problem that is used to do the 2-d Fourier transformation of Yukawa potential. We already know that $H_0(\frac{1}{z^2 + r^2}) = K_0(kz)$. Then what should be the right ...
2
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1answer
116 views

On shell and off shell simultaneously?

I am considering the following one loop virtual correction in the DIS process: where I have a quark of momentum $p$ coming in, emitting a gluon before interacting with a photon of momentum $q$ to ...
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1answer
194 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
6
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1answer
380 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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2answers
424 views

How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
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1answer
40 views

Yukawa Potential in non-relativistic limit

In Peskin's book "An Introduction to Quantum Field Theory", on page 121 (section 4.7) , it tries to recover the Yukawa Potential in the nonrelativistic limit, but there's a simplification that I don't ...