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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What is the path integral exactly?

I asked a question here about path integrals and QFT. I just want to confirm something. Is the path integral in quantum field theory a mathematical tool only? I thought the path integral meant that ...
4
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3answers
773 views

Quantum field theory, particle interpretations and path integrals?

I am trying to find some names or models of a particle interpretation of quantum field theory which isn't a literal path integral approach? Are there any particle interpretations of quantum field ...
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1answer
355 views

Renormalization: Why is only a finite number of counter-terms allowed?

I have a question please about renormalization in QFT. Why a renormalizable theory requires only a finite number of counter-terms?
4
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2answers
962 views

Field operator in Schrödinger picture

In Schrödinger picture operators do not depend on time explicitly. Consider a free scalar field with Lagrangian density $${\cal L} ~=~ \frac{1}{2}\partial_{\mu} \phi\partial^{\mu}\phi-\frac{m^2}{2}\...
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2answers
671 views

Algebraic/Axiomatic QFT vs Topological QFT

Can anybody please tell me a good source investigating the relation between Algebraic/Axiomatic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT)? Or is there none?
8
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1answer
506 views

Is this field redefinition for free scalar field theory non-local?

The action of free scalar field theory is as follows: $$ S=\int d^4 x \frac{\dot{\phi}^2}{2}-\frac{\phi(m^2-\nabla^2)\phi}{2}. $$ I have been thinking to redefine field as $$\phi'(x)=\sqrt{m^2-\nabla^...
13
votes
2answers
765 views

Gauge invariance and diffeomorphism invariance in Chern-Simons theory

I have studied Chern-Simons (CS) theory somewhat and I am puzzled by the question of how diff. and gauge invariance in CS theory are related, e.g. in $SU(2)$ CS theory. In particular, I would like to ...
16
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1answer
1k views

What really are superselection sectors and what are they used for?

When reading the term superselection sector, I always wrongly thought this must have something to do with supersymmetry ... DON'T laugh at me ... ;-) But now I have read in this answer, that for ...
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1answer
592 views

Klein-Gordon Canonical Commutation Relation (CCR)

In the complex Klein-Gordon field we regard as dynamical variables the field $\phi$, the complex conjugate of the field $\phi^*$, and the momenta $\pi$, $\pi^*$. I can't see how should arise the (...
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1answer
2k views

How many quarks in a proton?

I am confused by different papers I have seen on the internet. Some say there are three valence quarks and an infinite of sea quarks in a proton. Others say there are 3 valence quarks but a large ...
4
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1answer
272 views

State space of QFT, CCR and quantization, and the spectrum of a field operator?

In the canonical quantization of fields, CCR is postulated as (for scalar boson field ): $$[\phi(x),\pi(y)]=i\delta(x-y)\qquad\qquad(1)$$ in analogy with the ordinary QM commutation relation: $$[x_i,...
6
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1answer
549 views

Using $\frac{1}{A+i\epsilon} = PV\frac{1}{A}-i\pi\delta(A)$ in Feynman Integrals

Are the following operations O.K.? This is related to the Feynman parameter trick. $$F:= \int_0^1 \mathrm{d}x\int_0^{1-x}\mathrm{d}y \frac{1}{f(x,y)+\mathrm{i}\epsilon}.$$ Now using $$\frac{1}{A+i\...
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2answers
198 views

Regarding real field Klein Gordon Equations

Here are 2 doubts: If we change the sign of the mass term in the free massive KG Lagrangian to get: $L = \frac{1}{2}\partial^\mu\phi\partial_\mu\phi + \frac{1}{2}m^2\phi^2$, What would be the $...
7
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1answer
326 views

What do the modes of fermion fields look like?

A boson field can be understood as a collection of stationary modes (e.g. plane waves of various polarizations), and for each mode there is a quantum harmonic oscillator. If the QHO for some mode is ...
7
votes
1answer
218 views

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 ...
9
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3answers
486 views

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
586 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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0answers
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 ...
14
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1answer
764 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 ...
2
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4answers
1k views

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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1answer
434 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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1answer
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
699 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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1answer
487 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
390 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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1answer
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[\...
26
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1answer
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 ...
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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
votes
2answers
910 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
votes
0answers
130 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
390 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
1k views

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
412 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 ...
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2answers
177 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?
5
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1answer
420 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}}\...
4
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0answers
460 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
315 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
330 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
votes
2answers
598 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
votes
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
votes
3answers
178 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 $\omega$?
16
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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 $(+---)$ ...
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1answer
155 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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3answers
269 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
312 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
89 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
585 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?