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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Why is the majorana particle a fermion?

My knowledge of quantum mechanics is rather limited, but what I always understood was that Bosons have integer spins and Fermions have half-integer spins. My question is very simple: the Majorana ...
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three-particle quantum entanglement

So I know that two particles can be entangled in a quantum way, but is it possible that more than two particles be entangled in a quantum way? Most descriptions provide with two-particles cases, so I ...
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506 views

How does locality decouple the UV and IR behaviour of a QFT?

I came a comment in this paper: Scattering Amplitudes and the positive grassmannian in the last paragraph of page 104 which says: "One of the most fundamental consequences of space-time locality is ...
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514 views

Does the Standard Model have a Landau pole?

I have seen the statement that the Standard Model has a Landau pole, or at least it its believed that it does at $\sim 10^{34}$ GeV. Has this actually been proven (at least in perturbation theory, as ...
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255 views

A classically trivial quantum field theory of electromagnetism

Presumably there is a field theory of electromagnetism that classically gives trivial equations of motion, but when quantized shows interesting topological phenomena. I am talking about the Lagrangian ...
2
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3answers
759 views

Effective operator in four-fermion interaction

In one book, I have got the following lines which I found myself unable to understand what is effective operator? The paragraph is given below: The weak interaction describes nuclear beta decay, ...
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677 views

Spontaneous breaking of Lorentz invariance in gauge theories

I was browsing through the hep-th arXiv and came across this article: Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 ...
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350 views

Creation and Annihilation operator [closed]

In this page I want to know, why the equation (1.32) introduced creation and annihilation operator. Please elaborate.
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260 views

Fermion derivative coupling in QFT

I'm interested in a QFT model featuring a fermion derivative coupling like $XX^* \chi^*\gamma^\mu∂_\mu \psi$ where X is some other field operator. Has anybody seen a paper containing something like ...
2
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1answer
113 views

Induce a Fayet-Iliopoulos term

In a supersymmetric U(1) gauge theory, if I leave off the Fayet-Iliopoulos term $\kappa [V]_D$, what keeps it from being induced in loop corrections?
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232 views

Field energy of/from virtual Photons

I have a slightly out-of line question: Consider a single electron (or it's current if you please) The STATIC ELECTROMAGNETIC field surrounding it will (no doubt) have a field energy (T) to go with. ...
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341 views

Difficulties with bra and ket notation

I have problem in understanding equation (1.23), I croped this image from Mark_Srednicki "Quantum field theory". Can anyone show me the reason for the equation (1.23)?
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128 views

CP-violation in SUSY QED?

I have just gone through the exercise of constructing the supersymmetrized QED action. In the end, I get a reasonable action which matches literature. But after a little analysis, I find that the ...
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117 views

Trouble following the Saclay method (spectral representation of thermal Green functions)

Note: I just answered my own mathematical question by writing it up, but I thought I'd share it anyway in case someone else has a similar difficulty. :) I'm still left with my real physical question: ...
4
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161 views

Dimensional transmutation in Gross-Neveu vs others

Firstly I don't know how generic is dimensional transmutation and if it has any general model independent definition. Is dimensional transmutation in Gross-Neveau somehow fundamentally different ...
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1answer
263 views

Scalar field lagrangian and potential

This question is a continuation of this Phys.SE post. Scalar field theory does not have gauge symmetry, and in particular, $\phi\to\phi−1$ is not a gauge transformation. but why? and I want see the ...
5
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493 views

Defining a CFT using beta-functions

Won't it be correct to define a CFT as a QFT such that the beta-function of all the couplings vanish? But couldn't it be possible that the beta-function of a dimensionful coupling vanishes but it ...
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Why use Fourier expansion in Quantum Field Theory?

I have just begun studying quantum field theory and am following the book by Peskin and Schroeder for that. So while quantising the Klein Gordon field, we Fourier expand the field and then work only ...
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52 views

Is Inflation modelled by a field?

If Inflation is modelled by a field - is this a classical field or a quantum field? If classical are there good reasons not to quantise it? What are the implications of such a quantisation?
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304 views

Negative energy and large-scale spacetime structure

I was reading an essay from Stephen Hawking's on the Space and Time warps and I was trying to make sense on some statements referring to the Casimir effect such as: The energy density of empty ...
6
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939 views

Lorentz transformation of classical Klein–Gordon field

I'm trying to see that the invariance of the Klein–Gordon field implies that the Fourier coefficients $a(\mathbf{k})$ transform like scalars: $a'(\Lambda\mathbf{k})=a(\mathbf{k}).$ Starting from the ...
6
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174 views

Are group representations possible when the solution space is not a vector space?

As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
6
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247 views

Reference on Chern-Simons theory [duplicate]

I have recently been trying to refresh my memory on the Quantum Field Theory I learned 25 years ago while getting my Ph. D. At the time I did not study Chern-Simons modifications to QFT Lagrangians. ...
11
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337 views

Chiral perturbation theory: what is the Quark Condensate? why expand in $U$ rather than Goldstone fields?

I'm studying Chiral Perturbation Theory ($\chi PT$) from Scherer's Introduction to Chiral Perturbation Theory. What I am currently having some trouble understanding are two things: The quark ...
2
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1answer
703 views

What is the mathematical background needed for quantum physics? [duplicate]

I'm a computer scientist with a huge interest in mathematics. I have also recently started to develop some interest about quantum mechanics and quantum field theory. Assuming some knowledge in the ...
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In QFT, why does a vanishing commutator ensure causality?

In relativistic quantum field theories (QFT), $$[\phi(x),\phi^\dagger(y)] = 0 \;\;\mathrm{if}\;\; (x-y)^2<0$$ On the other hand, even for space-like separation $$\phi(x)\phi^\dagger(y)\ne0.$$ ...
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Trace of stress tensor vanishes ==> Weyl invariant

You often see in textbooks the statement that ${T^\mu}_\mu = 0$ implies Weyl invariance or conformal invariance. The proof goes like $\delta S \sim \int \sqrt{g} T^{\mu\nu} \delta g_{\mu\nu} \sim \...
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What is the Lagrangian from which the Klein-Gordon equation is derived in QFT?

Is there a well-known Lagrangian that, writing the corresponding eq of motion, gives the Klein-Gordon Equation in QFT? If so, what is it? What is the canonical conjugate momentum? I derive the same ...
2
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1answer
622 views

Dirac trace theorem

I am unable to prove exactly one trace identity that appears in the appendix of Peskin and Schroeder's QFT book. Can someone help me? The theorem [Appendix A.4 eqn (A.28)] says that the order of $\...
3
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1answer
228 views

Supersymmetric Sigma Model

I was working through the Mirror Symmetry book by Clay Math Institute. It deals with supersymmetric sigma model in 10.4 section. It doesn't derive how the action is invariant under the variation. I am ...
10
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496 views

About defining “baryons” and “mesons”

I want to understand the proof of the claims (of the construction as well as of its uniqueness) of gauge singlet states given around equation 2.13 (page 10) of this paper. Also does the listing of ...
3
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1answer
516 views

Wick Rotation, interpretation of $\bar{p}^2$ vs the usual $p^2=m^2$

Suppose we use the metric $(+,-,-,-)$ thus the momentum squared is $p^2 = p_0^2-\vec{p}^2 = m^2>0$ Defining $p_E:=\mathrm{i}\cdot p_0$ and $\bar{p}:=(\,p_E,\vec{p})$ with Euclidean norm $\bar{p}...
2
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1answer
419 views

Derivation of master equation

In this article* I want to get the Equation(9) with comparing the equation (2). Please elaborate the left side of equation (9). *Small amplitude quasi-breathers and oscillons by G. Fodor, et al. ...
2
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1answer
929 views

Interaction potential in standard $\phi^4$ theory

In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by $$S=\int d^d\! x \left[\frac12(\partial_\mu\phi)^2-U(\phi)\right],$...
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Are QFT solitons expected to represent standard model particles? Or strings?

Is work on solitons in QFT's focused on finding solutions that could represent the fundamental particles of the Standard Model, or is the work focused on finding particles Beyond The Standard Model? ...
13
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Why is the Yang-Mills gauge group assumed compact and semi-simple?

What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories? I'd think that these hypotheses lead to physically "...
2
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257 views

How is the hierarchy problem consistent with the decoupling theorem?

One the one hand we have the hierarchy problem in it's various forms, in my understanding in it's most serious form one could state it as the observation that if there is a heavy mass scale M in ...
20
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454 views

Anomalous target space diffeomorphisms for one-loop world-line integrals

The Schwinger effect can be calculated in the world-line formalism by coupling the particle to the target space potential $A$. My question relates to how this calculation might extend to computing ...
3
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1answer
287 views

Nonpertubative renormalization in quantum field theory versus statistical physics

I am trying to work my head around how renormalization works for quantum field theory. Most treatments cover perturbative renormalization theory and I am fine with this approach. But it is not the ...
6
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451 views

What are the mathematical prerequisites to understand this paper? [closed]

What are the mathematical prerequisites to understand this paper? Blumenhagen et al. Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes. Phys. Rept. 445 no. 1-6, pp. ...
7
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1answer
369 views

Theories with non-vanishing commutators outside the lightcone

I'm reading Weinberg's new book on Quantum Mechanics, and in Chapter 8.7 "Time-Dependent Perturbation Theory" he derives the usual Dyson series for the $S$ matrix when the interaction Hamiltonian $V_I(...
5
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1answer
958 views

Why do disconnected diagrams not contribute to the S matrix?

I've read somewhere that disconnected diagrams do not contribute to the S-matrix. I don't see why this is the case. I do know why vacuum bubbles do not contribute: given a generating functional for a ...
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1answer
192 views

Divergence in Supergravity

I'm not familiar with supergravity so here's my question: I've heard in talks that if one finds divergence for five-loop 4-graviton scattering amplitudes in five dimensions this translates to a ...
7
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2answers
420 views

Complex coordinates in CFT

The Setup: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric $ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$. It seems to me that ...
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235 views

Range of forces from mass of force carrier?

Why is $\frac{\hbar}{mc}$ a good estimate of the range of the four forces, where $m$ is the mass of the carrier particle of the force? Inputting the pion mass gives $1.4\ \mathrm{fm}$ for the hadronic ...
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79 views

Interaction energy calculation in QFT

Suppose I have a QFT action describing interaction of two objects and I can perturbative write the action as $S=S_0+S_i$ where $S_0$ is the non-interacting, unperturbed action and $S_i$ is the ...
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62 views

Do Boundary Conditions depend on spin connections for gauge fields?

In the article arXiv:1206.5642, which talks about gauge fields in conical spacetime, I came across the statement in footnote 4 that the boundary conditions on the gauge field depend on the spin ...
4
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1answer
591 views

Time-ordering in QFT [duplicate]

In Srednicki QFT page 37. In the derivation of LSZ reduction formula, he introduces the time-order operator $T$, so no time-dependent creation/annihilation operators are left in the transition ...
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Can mass dimension of a field be viewed as another 'quantum number'?

While studying SUSY in 4D, I noticed the dynamical chiral superfield has dimension [GeV], whereas the dynamical vector superfield (for gauge theories) is unitless. Because I was introduced to the ...
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Are irrelevant terms in the Kahler potential always irrelevant, even at strong coupling?

I've been reading about the duality cascade in Strassler's TASI '03 lectures (hep-th/0505153). He reminds us of the non-renormalization theorem theorem for the superpotential so that the beta ...