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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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 ...
5
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1answer
208 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 ...
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0answers
46 views

Chern Simons Theory over S^3 as integral - what is domain of integration?

I found these nice lecture notes Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories so I am hoping to understand some parts of the Chern Simons theory better. ...
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0answers
26 views

Linear term in six dimensional $\phi^3$-theory

In our current QFT homework we are given the following Lagrangian in six spacetime dimensions. It is $$ \mathcal L = \frac12 [\partial \phi]^2 - c_0 \phi - \frac{m_0^2}2\phi^2 - ...
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3answers
499 views

Effect of linear terms on a QFT

I was always told when first learning QFT that linear terms in the Lagrangian are harmless and we can essentially just ignore them. However, I've recently seen in the linear sigma model, ...
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30 views

Can virtual particles be thought of as pieces of 'nonregular' waves?

I just came across this blog post, which gives an interpretation of virtual particles I haven't seen before. To rephrase it, consider a 1D system of springs and masses, where the springs are slightly ...
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0answers
50 views

Green's functions and spectral function

I'm struggling to understand something in the book by Fetter & Walecka, p.295, relating to the causal ($G$), advanced ($G^A$) and retarded ($G^R$) Green's functions, and the spectral function ...
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1answer
37 views

electric field's area [closed]

How much area an electric field surrounds? since we're just able to draw the electric lines of force we sometimes think that the field is though 3d but surrounds a finite area.But is it measurable or ...
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0answers
61 views

Does this vertex equal 0?

If I have an interaction term in my Lagrangian that looks like: $\mathcal{L}_{int} = (\partial_\mu B_\nu)(A^\mu B^\nu - A^\nu B^\mu)$ where B is a massive spin-1 field. Am I correct in thinking that ...
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0answers
29 views

Doubts about quark confinement, the pole mass and the quark gluon plasma

I have seen written a few times that the notion of a pole mass for a quark contradicts the quark confinement picture and that non-perturbatively it is expected that the quark pole mass be infinite. ...
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1answer
49 views

Is there a correlation between Brownian motion and cosmic microwave background radiation?

Is there any correlation between Brownian motion, the phenomenon of osmosis - compared to cosmic microwave background, the Noise we see in analog television? Brownian motion or pedesis (from Greek: ...
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2answers
197 views

Pauli Villars Regularization

Consider the t-channel diagram of phi-4 one loop diagrams. Evaluated it is, with loop momenta p, $\frac{\lambda^2}{2}\displaystyle\int\frac{d^4p}{(2\pi)^4}\frac{1}{(p+q)^2-m^2}\frac{1}{p^2-m^2}$ If ...
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1answer
415 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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1answer
68 views

Coherent state path integral - derivation

I divided the time interval $[t_0=:t_i,t_f:=t_N]$ into $N$ steps $[t_{k-1},t_{k}],\, k=1,\dots, N$ and applied the resolution of unity for coherent states \begin{equation} ...
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0answers
39 views

Mode expansions of fields

This is a very simple question but would appreciate it if someone could clarify - I've heard different things from different people so I'm a little bit confused yet the question is simple: Given the ...
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0answers
66 views

Angular momentum of the vacuum

I'm studying quantum field theory from "An introduction to Quantum field theory" by Peskin and Schroeder and from "A modern introduction to quantum field theory" by Maggiore. I've read from "An ...
6
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1answer
404 views

Free Particle Path Integral Matsubara Frequency

I am trying to calculate $$Z = \int\limits_{\phi(\beta) = \phi(0) =0} D \phi\ e^{-\frac{1}{2} \int_0^{\beta} d\tau \dot{\phi}^2}$$ without transforming it to the Matsubara frequency space, I can ...
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0answers
61 views

Gauging a mixture of internal and spacetime symmetries

Given an internal symmetry, say $U(1)$ or $SU(2)$, I understand how to gauge it, by coupling the conserved current $J_{\mu}$ to a gauge field $A^{\mu}$. Similarly, I understand how to gauge a ...
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0answers
45 views

Calculation of divergences of Feynman diagram

In Peskin Schroeder, while considering gluon diagrams for $\beta$-function in QCD, they say that we can calculate the divergent part of loop diagram taking limit of zero external momenta - e.g. for ...
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1answer
1k views

Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
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1answer
66 views

Problem arising from quantisation of e.m. field

In my studies on the quantisation of the electromagnetic field I've come across a small calculation that I wasn't able to reproduce. Remember the following: In the Gupta-Bleuler method to quantize ...
6
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4answers
1k views

Why is normal ordering a valid operation?

Why is normal ordering even a valid operation in the first place? I mean it can give us some nice results, but why can we do the ordering for the operators like that? Is its definition motivated by ...
8
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1answer
362 views

Renormalization group resummation

I'm having trouble in understeanding a mathematical feature of RG, namely how it provides a way to resum the perturbation series and how that's defined mathematically. From a conceptual point of view ...
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0answers
34 views

S-matrix element for forward scattering and amputed green function

I'm studying dispersion relations applied as alternative method to perturbation theory from Weinberg's book (Vol.1) Let's consider the forward scattering in the lab frame of a massless boson of any ...
2
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1answer
94 views

Does scale invariance imply massless or continuous mass distribution?

$\newcommand{\ket}[1]{\lvert #1 \rangle}\newcommand{\bra}[1]{\langle #1 \rvert}\newcommand{\scp}[2]{\langle #1 \vert #2 \rangle}$ In his 2008 slides (PDF), Tzu-Chiang Yuan mentions the following on p. ...
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1answer
109 views

Why would a square matrix transform?

Why would a square matrix of spinless fields $\Lambda$ transform under symmetries? Given: $$\delta \psi_L = i \epsilon_L^aT_a\psi_L$$ and $$\delta \psi_R = i \epsilon_R^aT_a\psi_R$$
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2answers
186 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 ...
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0answers
46 views

Gravitational wave as a consequence of gravity being a field

I was reading an online article about gravitational wave detection and there is a sentence which says: The existence of gravitational wave is simply a consequence of the fact that gravity is a ...
4
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1answer
321 views

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
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6answers
2k views

How is the double slit experiment modeled in contemporary physical theories?

Suppose I have the following double split experiment set up: a monochromatic electron source of low intensity, which we can model as emitting a single electron at a time with energy $T$. a ...
24
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4answers
1k views

Regularization of the Casimir effect

For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
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vote
2answers
336 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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0answers
230 views

Heisenberg's Unified Field Theory

While searching in the Internet, I came to know about Werner Heisenberg's attempt to obtain an Unified Field Theory (see the book Introduction to Unified Field Theory of Elementary Particles). But ...
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1answer
224 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
38 views

Probability of $\alpha$-decay

In standard Gamow model we assume that $\alpha$ particle is already in the nucleus, i.e. four nucleons are "glued" together and this particle is emitted. So, we assume that the probability of the ...
5
votes
1answer
189 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
45 views

Why is the angular momentum added for two independent electron system? (no problem)

There is no problem now. But somebody may be confused by the same analysis when studying QM or Group theory. (actually my motivation for asking this question comes from the SU(5) Grand Unification ...
6
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2answers
369 views

Scalar field divergent mass correction interpretation question (hierarchy problem)

Simple power counting tells you that a scalar field coupled to some fermions at one-loop picks up a correction to the mass of the order $\Lambda^2$. Based on this people say things like "it's natural ...
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0answers
22 views

What are the actual conventions for the standard model particles' intrinsic parities?

It is known that by fixing the intrinsic parity of three particles with linearly independent quantum numbers B, L and Q, the other particles' parities are fixed by the request that parity be conserved ...
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0answers
18 views

zee model of radiative neutrino mass

Without computing the expression for radiatively generated neutrino mass matrix $M_{\alpha\beta}$, in Zee model, is it possible to guess that the diagonal elements of the mass matrix vanishes? I ...
3
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1answer
51 views

Decomposing massless N=8 SUGRA multiplet into multiplets of massless N=4

The only massless $N=8$ SUGRA multiplet is given by $(g_{\mu\nu},\psi_\mu^{\Sigma},A_\mu^{[\Sigma\Pi]},\chi_{\alpha}^{[\Sigma\Pi\Lambda]} ,\phi^{[\Sigma\Pi\Lambda\Omega]})$ where the greek upper ...
2
votes
1answer
115 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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0answers
61 views

Making mathematical sense on a Feynman's path integral equation

Usually we find this relation in the context of Feynman's path integral (see, for example, Maggiore's book on QFT, pg 223): $ \int_{q_i}^{q_f}[dq] = \int_{-\infty}^{\infty}d\bar{q}\int_{q_i}^{\bar ...
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0answers
21 views

Comoving and physical momentum in a Friedmann universe

It is most probably a very basic question, but I'm a bit stuck with it. Let us consider a spatially flat Friedmann universe with the usual metric ...
1
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1answer
25 views

Evaluating Compton scattering cross-section

In deriving the cross-section of Compton scattering, we require to perform the polarization sum $$\sum\epsilon_{\mu}\epsilon_{\nu}\sum\epsilon_{\alpha}\epsilon_{\beta}$$ using the identity ...
3
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0answers
30 views

Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
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1answer
72 views

What is spin in QFT, non-relativistic QM, and classical physics? When can we ignore spin? [closed]

In section 4.1.1 of quantum field theory book by M. Schwartz, the author wants to calculate electron scattering by photons and writes the following interaction: $$ V= \frac{1}{2}e\int dx ...
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1answer
260 views

effective field theory of the projective semion model

The "projective semion" model was considered in http://arxiv.org/abs/1403.6491 (page 2). It is a symmetry enriched topological (SET) phase. There is one non-trivial anyon, a semion $s$ which induces a ...
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0answers
51 views

How to relate classical field and quantum operator?

Recently I listened to a lecture from perimeter institute. There was an idea which I found interesting. That is, roughly, for a field $\phi(x)$ we can assume the relation with the creation operator ...
5
votes
2answers
281 views

Why does the non-linearity of the string action prohibit stretching due to strong excitations?

From 't Hooft's String Theory lecture notes on page 8 (paraphrased): To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and ...