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 ...

learn more… | top users | synonyms (1)

1
vote
2answers
21 views

Does Unitary operator take a pure state to a pure state or can it take a pure state to a mixed state?

Does Unitary operator take a pure state to a pure state or can it take a pure state to a mixed state? I think so but why? I assume the Unitary operator acts on a pure state only.
0
votes
1answer
45 views

Definition of the S-matrix

when I think about scattering process I reach to slightly another definition to the S-matrix. because I understand my reasoning I hope someone could refine it to a correct one so that I can have a ...
11
votes
1answer
477 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) = ...
0
votes
1answer
58 views

The $T\rightarrow \infty $ limit in quantum field theory

I am new to quantum field theory. Prior to this, I have been using quantum mechanics for a few years. I am reading the book by A. Zee, ''quantum field theory in a nutshell'', 2nd Ed.. On page 18, ...
3
votes
2answers
220 views

Weak interaction violate charge conjugate

How can we show that the weak interaction violates the charge conjugation symmetry?
4
votes
2answers
109 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 ...
3
votes
1answer
35 views

$W^{++}$ / $W^{--}$ Bosons in theory and experiment

I wonder whether there is any theoretical interest in and/or experimental search for double charged bosons, probably to be called $W^{++}$ and $W^{--}$. The latter would obviously turn an electron ...
2
votes
1answer
66 views

Why is Wick contraction a $c$-number?

It is mentioned in Fetter's Quantum Theory of Many-Particle Systems (in contraction part of section 8 Wick's Theorem), that: contractions are c numbers in the occupation-number Hilbert space, not ...
11
votes
2answers
519 views

What does an excitation in a field mean?

The term "field excitation" is used a lot especially when I hear about the Higgs boson. However, I cannot find an explanation of what precisely that means. I have a few questions relating to this. ...
2
votes
0answers
24 views

Integrating out heavy fields while preserving symmetries

The basic a-b-c for integrating out heavy fields what one learns when making the example of Fermi theory, is that if you have a Lagrangian $L= -\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+\frac{1}{2}M^2 V^\mu ...
4
votes
2answers
277 views

Why does Srednicki insist on $\phi$ having zero VEV?

Let $\phi$ be a scalar field in an interacting theory ($\phi^3$ or $\phi^4$, for example). If $|0\rangle$ is the vacuum of the interacting theory and $P^\mu$ is the four-momentum operator, we have ...
0
votes
1answer
33 views

Are pure Dirac fermions (electrons, quarks, …) allowed to have effective Majorana mass?

Charged particles such as electrons and quarks are not allowed to have a hard Majorana mass (see here). With 'hard' I mean an explicit mass term in the Lagrangian which would break the corresponding ...
0
votes
1answer
42 views

Scattering in Schrödinger picture

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 ...
1
vote
1answer
31 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 ...
0
votes
0answers
22 views

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 ...
1
vote
2answers
239 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 ...
0
votes
0answers
15 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 ...
-1
votes
1answer
38 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?
0
votes
1answer
112 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 ...
1
vote
1answer
27 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.
10
votes
1answer
590 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 ...
0
votes
0answers
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?
0
votes
0answers
31 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 ...
1
vote
0answers
19 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? ...
2
votes
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, ...
6
votes
1answer
511 views
2
votes
1answer
136 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 ...
7
votes
2answers
54 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
votes
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 ...
-3
votes
1answer
63 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 ...
8
votes
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 ...
4
votes
1answer
92 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 ...
0
votes
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 ...
0
votes
0answers
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 ...
0
votes
0answers
69 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 $p^0$ ...
3
votes
0answers
42 views

Higgs mechanism in quantum GLSM

My question is regarding the following Gauged Linear Sigma Model (GLSM) in two dimensions. $$\tag{1} S=\int d^2x\Big(-D_{\mu}\overline{\phi} D^{\mu}\phi +\frac{D^2}{2e'^2} +D(|\phi|^2-r)\Big).$$ ...
7
votes
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 ...
3
votes
0answers
35 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 ...
1
vote
0answers
42 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 ...
7
votes
3answers
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}) ...
12
votes
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 ...
13
votes
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 ...
41
votes
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 ...
-1
votes
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?
2
votes
1answer
104 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 ...
1
vote
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
votes
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 ...
-3
votes
0answers
29 views

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
votes
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 ...
3
votes
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 ...