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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topological twisting by introducing bosonized operator

In this paper http://arxiv.org/abs/hep-th/9309140 on page 125, the authors claim that one can twist the $N=2$ theory by introducing a term in the action $\frac{1}{2}\int R \phi$, where $\phi$ is the ...
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Chern-Simons degrees of freedom

I'm currently reading the paper http://arxiv.org/abs/hep-th/9405171 by Banados. I am just getting acquainted with the details of Chern-Simons theory, and I'm hoping that someone can explain/elaborate ...
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2answers
575 views

Can't find the mass scale; calculation using the modified minimal subtraction scheme and dimensional regularisation

I am taking a course on quantum field theory where there is some confusion regarding the renormalisation scheme we are using (and a corresponding one in my mind). Apparently the lecturer meant MS-bar ...
6
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82 views

axial and vector resonances in composite higgs models

Is there a reason to believe that the axial resonances be heavier than the vector resonances in the composite higgs models? For instance, in http://arxiv.org/abs/0808.2071, to have zero tree level ...
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1answer
1k views

Why path integral approach may suffer from operator ordering problem?

In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path. What did ...
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742 views

Why do irrelevant operators require infinitely many counterterms?

As far as I understand it, in the Wilsonian picture of renormalization, we view a theory as having some fixed cutoff and bare couplings, and integrate out high-momentum modes to understand what ...
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4answers
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How Uncertainty Principle, Vacuum fluctuations and Energy Conservation coexist in QFT?

Recently I had a debate about the uncertainty principle in QFT that made me even more confused.. Because we use Fourier transforms in QFT, we should have an analogue to the usual Heisenberg ...
6
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431 views

Database of scattering amplitudes

I want to check whether my result for the invariant amplitude of the electron-electron scattering (to lowest order in $\alpha$; t+u channels) is correct or not. I can't find any reference that has ...
25
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704 views

Sigma Models on Riemann Surfaces

I'm interested in knowing whether sigma models with an $n$-sheeted Riemann surface as the target space have been considered in the literature. To be explicit, these would have the action \begin{align*}...
6
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2answers
687 views

Causality and Quantum Field Theory

I have a problem with proof of causality in Peskin & Schroeder, An Introduction to QFT, page 28. To avoid confusion I use three vectors notation, rewriting the Eq. (2.53) for $y=0$ as follows: $[\...
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484 views

Can modern twistor methods to calculate scattering amplitudes be applied to renormalization group calculations?

As explained for example in this article by Prof. Strassler, modern twistor methods to calculate scattering amplitudes have already been proven immensely helpful to calculate the standard model ...
3
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1answer
389 views

Crazy Dirac Deltas

I'm not expecting any rigor in the following and the answers...since we're dealing with Dirac deltas in the context of QFT. Consider the integral $$ \int d^4q\ \Theta(q_0)\Theta(p_{3,0}+q_0)\ \...
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99 views

How the nonlinear equation can be written like this?

We consider a scalar theory in a $1+D$ dimensional flat Minkowski space-time, with a general self-interaction potential, whose action can be written as \begin{equation} A=\int dt\, d^D\! x \left[\...
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2k views

Emergent symmetries

As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
1
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1answer
248 views

Interaction potential analysis from $\phi^4$ model

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],$...
8
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2answers
896 views

Does Dirac's idea of filled negative energy states make sense?

Please bear with me a bit on this. I know my title is controversial, but it's serious and detailed question about the explanation Dirac attached to his amazing equations, not the equations themselves. ...
6
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129 views

Is the search for a Simple-group-based Electro-Weak theory over?

Just wondering: We know that, in its current form of the $SU(2)_L\times U(1)$, the electroweak theroy rides a wave of huge success. However, is it not possible that the correct simple group ...
5
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2answers
385 views

Correlation, Time Ordering, and Observables

In general, the product of two Hermitian operators $\phi$ will not be Hermitian, unless the two operators commute. Question: is $X = T \phi(t_1) \phi(t_2)$ Hermitian? It doesn't seem to be if $T \...
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4answers
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Could all strings be one single string which weaves the fabric of the universe?

This question popped out of another discussion, about if the photon needs a receiver to exist. Can a photon get emitted without a receiver? A universe containing only one electron was hypothetically ...
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0answers
75 views

What are the U(x) and V(x-y)

Srednicki in his QFT book introduces the the Hamiltonian operator of the quantum field theory (equation 1.32). Here what are $U \bf(x)$ and $V\bf(x-y)$?
6
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1answer
408 views

Is the quantization of gravity necessary for a quantum theory of gravity? Part II

(At the suggestion of the user markovchain, I have decided to take a very large edit/addition to the original question, and ask it as a separate question altogether.) Here it is: I have since ...
2
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2answers
175 views

Definition of Free field or Noninteracting field

In QFT we can write a Hamiltonian operator for a free field. So, what is a free field/ noninteracting field?
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415 views

Deriving the reduced Green's functions in Polchinski's volume 1

In equation 6.2.7, Polchinski defines his reduced Green's functions $G'$ on the 2-manifold to satisfy the equation, $$ \frac{-1}{2\pi \alpha '}\nabla ^2 G'(\sigma_1, \sigma_2) = \frac{1}{\sqrt{g}}\...
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456 views

Mathematics and Physics prerequisites for mirror symmetry [closed]

I am a physics undergrad interested in Mathematical Physics. I am more interested in the mathematical side of things, and interested to solve problems in mathematics using Physics. My current ...
2
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2answers
314 views

Dark matter and QFT

My understanding is that the particle is a somewhat artificial notion in QFT (see: Quantum Mechanics: Myths and Facts), and that in general it is possible for a quantum field to have unstable ...
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2answers
328 views

Ontology of the quantum field

I'll use QED as an example, but my question is relevant to any quantum field theory. When we have a particle in QED, where is its charge contained in the field? Is the field itself charged? If so, ...
3
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597 views

Hawking Radiation: how does a particle ever cross the event horizon?

The heuristic argument for Hawking Radiation is, that a virtual pair-production happens just at the event horizon. One particle goes into the black hole, while the other can be observed as radiation. ...
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2answers
116 views

If a particle is a point of high intensity in a quantum field, how can it have charge?

The charge of a fundamental particle is a mysterious but obvious and well-known property of every non-neutral particle. I can understand how, if a particle is an object, or thing, for want of a ...
6
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1answer
2k views

Loop integral using Feynman's trick

I am trying to show for the one-loop integral with three propagators with different internal masses $m_1$, $m_2$, $m_3$, and all off-shell external momenta $p_1$, $p_2$, $p_3$ the following formula ...
4
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3answers
177 views

Reason for considering the positive root

In eqn. (3.11) of Srednicki's QFT book only the positive root is considered; i.e., $ \omega = + \sqrt{(k^2 + m^2 )} $ Why the negative root is not considered? And what is the $\omega$?
15
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2answers
2k views

Gauge covariant derivative in different books

It puzzles me that Zee uses throughout the book this definition of covariant derivative: $$D_{\mu} \phi=\partial_{\mu}\phi-ieA_{\mu}\phi$$ with a minus sign, despite of the use of the $(+---)$ ...
0
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1answer
154 views

Oscillon and soliton

I want to know the major difference between oscillon and soliton in terms of radiating energy with respect to time and position. And what about their localization?
2
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267 views

Equivalence between QFT and many-particle QM

My understanding from my QFT class (and books such as Brown), is that many-particle QM is equivalent to field quantization. If this is true, why is it not an extremely surprising coincidence? The ...
3
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1answer
308 views

Definition of Local Function

Now a days I am studying Srednicki's QFT book. In its third chapter it is written that Any local function of φ(x) is a Lorentz scalar, [...] . Now my question is: What is a local function?
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1answer
88 views

Question about Ryder text (Generating functional)

The second equality in (6.88) he says was obtained by expanding the denomitator by the binomial theorem. It is probably very dumb but I'm not following. I see how the 1 and the vacuum term in the ...
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0answers
572 views

How is the term “Born level” usually defined?

How is the term "Born level" usually defined, e.g. in talking about the $pp\to Z/\gamma^*\to e^+e^-$ cross section at Born level?
10
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1answer
274 views

Non-covariance of the higher rank propagator (from Weinberg's QFT textbook)

In chapter 6.2 of Weinberg's QFT Vol.1, he gave the general form of Wick contractions of all possible fields(scalar, spinor, vector, etc.), he showed $$\Delta_{lm}(x,y)=\theta(x-y)P^{(L)}_{lm}\left(-...
16
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3answers
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In what sense is a scalar field observable in QFT?

Consider a QFT consisting of a single, hermitian scalar field $\Phi$ on spacetime (say $\mathbb R^{3,1}$ for simplicity). At each point $x$ in spacetime, $\Phi(x)$ is an observable in the sense that ...
5
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1answer
388 views

What is generalized free field?

I came across the term generalized free field in a paper recently but I don't know its definition. Google leads to other papers which take it for granted and use it without defining it. It appears ...
18
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1answer
675 views

Does local physics depend on global topology?

Motivating Example In standard treatments of AdS/CFT (MAGOO for example), one defines $\mathrm{AdS}_{p+2}$ as a particular embedded submanifold of $\mathbb R^{2,p+1}$ which gives it topology $S^1\...
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531 views

Starting string theory studies in grad school

How is it possible for a grad student to do research in any modern area of string theory like AdS/CFT or ABJM if they need to start grad school by having to learn QFT from scratch? Is there a time-...
7
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1answer
1k views

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 ...
3
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1answer
2k views

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 ...
6
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2answers
503 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 ...
7
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1answer
506 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 ...
2
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1answer
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
748 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, ...
16
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1answer
671 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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1answer
256 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 ...