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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Scattering in Schrödinger picture [closed]

If we look at a scattering process in the Schrödinger picture for a Hamiltonian $H = H_0(t) + V(t)$ where $H$ is independent of time (because we examine a theoretical situation after accelerating ...
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1answer
42 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
253 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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28 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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43 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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119 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
35 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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600 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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27 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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24 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
136 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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513 views

How to compute the normal ordered angular momentum of a Klein-Gordon real scalar in terms of ladder operators?

I'm trying to compute the angular momentum $$Q_i=-2\epsilon_{ijk}\int{d^3x}\,x^kT^{0j}\tag{1}$$ where ${T^\mu}_\nu=\frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}\partial_\nu\phi-{\delta^\mu}_\...
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65 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 ...
2
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1answer
313 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
69 views

Is there one wavefunction per field? [closed]

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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1answer
96 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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22 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 ...
3
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0answers
55 views

Higgs mechanism in quantum GLSM

My question is regarding the following Gauged Linear Sigma Model (GLSM) in two dimensions. $$\tag{1} S=\int d^2x\Big(-D_{\mu}\overline{\phi} D^{\mu}\phi +\frac{D^2}{2e'^2} +D(|\phi|^2-r)\Big).$$ ...
2
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0answers
56 views

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 ...
8
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3answers
201 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}) \vec{a}^\dagger(\vec{...
12
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1answer
189 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 ...
13
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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 ...
2
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1answer
110 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
118 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
60 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 ...
3
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1answer
64 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
28 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 d^4x[-V_{eff}(\phi_c)+Z(\...
3
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1answer
58 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 d^4x(\mathcal{L}(\phi)+...
6
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1answer
272 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 $ \...
2
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1answer
126 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 ...
6
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1answer
385 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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1answer
45 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 ...
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1answer
208 views

Derivation of eq 6.17, Peskin and Schroeder [closed]

I am having trouble following a derivation in Peskin and Schroeder's textbook, namely equation 6.17 on page 182. It seems benign at first, but I am completely stuck. Essentially, we have an expression ...
7
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1answer
292 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
3
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1answer
79 views

Anomaly, Ward identity [closed]

While studying notes on anomaly by Adel Bilal (http://arxiv.org/abs/0802.0634), I stuck in a calculation. Here it goes as follows: The three-current correlator in perturbation theory as a one-loop ...
2
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0answers
56 views

Determinants in path integrals in gauge theories and geometry

I know that in the formalism of path integral it is easy to show how determinants, corresponding to gauge fixing condition and FP ghosts, appear. But there is strict explanation of these determinants ...
6
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1answer
297 views

What is meant by the term “value” of a scalar quantum field?

During the slow roll of a scalar field, the scalar field is changing its value over time. But what is meant by the term "value" of a scalar field? Since the scalar field is quantized, I don't ...
3
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0answers
86 views

Simple, physical explanations for Hadamard behaviour of two-point functions

The two-point function of local quantum fields on a curved spacetime exhibits a singularity of a very particular form, known as Hadamard form, for null separated points $(x,y)$ (including the ...
15
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2answers
919 views

Rest mass of phonon: is this concept definable?

Phonons are obtaied by non-relativistic quantization of the lattice vibration. The dispersion relation is given by $\omega=c_s k$ where $c_s$ is the velocity of sound. What can we say about the mass ...
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0answers
74 views

“Constant Fermion”

I was talking to a professor in my institution which works in Lorentz Violation of various QF theories. While we talk about a SUSY lagrangian, I asked him if we could have a fermion acquiring VEV and ...
3
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1answer
31 views

Reaching equilibrium in a blackbody and light-matter interaction

Suppose we have a metallic cavity maintained at a fixed temperature. Suppose we start with any distribution of radiation that is not in equilibrium with the container. Gradually, when the equilibrium ...
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0answers
37 views

Quartic interactions of a complex scalar field

For a quartic self-interaction of a complex scalar field (matrix), one can write the terms: $aTr((\phi^*\phi)^2)$ and $bTr(\phi^*\phi)^2$ ; the trace and the "double" trace term, with two different ...
0
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1answer
35 views

Inner product of standard-momentum one-particle states in Weinberg

My question has essentially already been addressed in Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT (third question), but unfortunately ...
5
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1answer
125 views

Physical interpretation of the retarded vs. Feynman propagators?

We calculate the real-space propagator $\Delta(x)$ for a free real scalar field $\varphi(x)$ with mass $m$ by performing the Fourier transform (using sign convention +---) $$\Delta(x) = \int \frac{d^...
3
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1answer
158 views

What justifies the dependence of the coupling renormalization constant in the dimensional regularization regulator?

I wanna clarify some issues about renormalization in the $\bar{MS}$ scheme that I glossed over when I first learnt about this stuff. I am following http://arxiv.org/abs/1411.7853 section 3.1. The ...
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1answer
58 views

With the descent of Newtonian mechanics is Newton's third law still valid?

Or more specifically, with the standard model, quantum theory and other advances in physics, all those experiments in CERN and other accelerators, was there any occurrence where this law was violated? ...