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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Regulating the sum in Casimir Force

I am trying to evaluate the Casimir force using a Gaussian regulator (I know there are other much easier ways to do this, but I want to try this!) We then are reduced to evaluating the sum $$ ...
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92 views

Translate a two dimensional classical Dirac theory to a (1+1)-dim quantum theory

Suppose I have a two dimensional classical Dirac Hamiltonian with $\Psi=(\psi_1,\psi_2)^T$: $$ H=\int \mathrm{d}x \mathrm{d}y \Psi^\dagger(\sigma^x i\partial_x+\sigma^y i\partial_y+m\sigma^z)\Psi. $$ ...
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1k views

The analogy between temperature and imaginary time

There are many statements about the relation between time and temperature in statistical physics and quantum field theory, the basic idea is to interpret (inverse) temperature in statistics as "time" ...
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1answer
196 views

Glueball mass in non-abelian Yang Mills theory

How can the glueball mass be calculated in Yang Mills theory?
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1answer
177 views

Why Must Conserved Currents of Lorentz Symmetry Satisfy the Lorentz Algebra

I've seen it written many times that the commutation relation $[M^{I-},M^{J-}]=0$ is required for Lorentz invariance in the light cone gauge quantisation of the bosonic string. This follows ...
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216 views

Inner product of particle-anti-particle spinor components

Suppose I have four-component spinors $\Psi$ and $\bar \Psi$ satisfying the Dirac equation with $$\Psi(\vec x) = \int \frac{\textrm{d}^3 p}{(2\pi)^3} \frac{1}{\sqrt{2 E_{\vec p}}} \sum_{s = \pm ...
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413 views

How do I define time-ordering for Wightman functions?

This is a follow-up question to What are Wightman fields/functions Ok, so based on my reading, the field operators of a theory are understood to be operator-valued distributions, that is, to be ...
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228 views

Interacting representation of the Poincaré group

In his QFT book, Weinberg claims what follows (Vol I, pag. 144-145): given a (free) representation of the Poincaré group with generators $\bf P$ (spatial translations), $H_0$ (time translations), $\bf ...
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275 views

Unstable particles and quantum field theory

I am searching for not too old literature on the quantum description of unstable particles. I am referring to something beyond the ad-hoc S-matrix description based on the optical theorem common to ...
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672 views

Applications of QFT in theoretical physics

I would like to know which fields in physics have seen growth or benefited by applying QFT? I know that approaches to quantum gravity such as string theory use QFT, HEP and also some branches of ...
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173 views

How does relativity lead to multi particles in Dirac and QFT, exactly

I have asked this question before on other forums, but only got the classical answer of the impossibility of the probability interpretation for single particle in QFT. Now, there seems to be also ...
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258 views

alternatives to supersymmetry and Coleman-Mandule theorem

Humour me for a minute here and let's imagine that all interesting and plausible supersymmetry models have been "cornered" out by the experimental data; what sort of alternatives are there for having ...
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640 views

Faddeev-Popov ghost propagator in canonical quantization

Obtaining the propagator for the Faddeev-Popov (FP) ghosts from the path integral language is straightforward. It is simply $$\langle T(c(x) \bar c(y))\rangle~=~\int\frac{d^4 p}{(2\pi)^4}\frac{i ...
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171 views

Poincaré group on quantum Klein-Gordon field (C*-algebraic scenario)

on the same topic as this question, I have been trying to fool around with the free real K-G field in flat spacetime on the C*-algebraic scenario (Haag-Kastler axioms, Weyl quantization, etc). Since ...
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510 views

Why is the axial current said to create particles?

In Peskin and Schroeder p. 669 it is argued that the axial current can be parametrized between the vacuum and an on-shell pion state as: $$<0|j^{\mu 5}(x)|\pi^b(p)>=-ip^\mu f_\pi ...
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Interpretation of derivative interaction term in QFT

I am trying to understand what a term like $$ \mathcal{L}_{int} = (\partial^{\mu}A )^2 B^2 $$ with $A$ and $B$ being scalar fields for instance means. I understand how to draw an interaction term in ...
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991 views

What is the relativistic particle in a box?

I know people try to solve Dirac equation in a box. Some claim it cannot be done. Some claim that they had found the solution, I have seen three and they are all different and bizarre. But my main ...
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203 views

Many faces of linear response theory

I have seen two forms of linear response: One is in the calculation of susceptibilities using Green functions. The other is in the evaluation of response currents, say, London current of a ...
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965 views

What are Wightman fields/functions

Simple question: What are Wightman fields? What are Wightman functions? What are their uses? For example can I use them in operator product expansions? How about in scattering theory?
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2answers
381 views

What is the exact relationship between scale invariance and renormalizability of a theory?

I have often read that renormalizability and scale invariance are somehow related. For example in this tutorial on page 12 in the first sentence of point (7), self similarity (= scale invariance ?) is ...
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2answers
538 views

How do I derive the transformation law of a Weyl spinor under a Lorentz transformation?

Let $\xi$ be a spinor. If $(\theta ,\phi)$ are the parameters of a rotation and pure Lorentz transformation, then how can we prove that the transformation rule for $\xi$ can be written as $$\xi ...
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1answer
270 views

Geometric interpretation of perturbation theory in quantum field theory

I am studying GR right now, and one interesting thing I learned about vectors is that they are defined to have the same properties as derivatives. With this in mind, can I make a differential ...
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1answer
230 views

Generalizations of Bell's inequality to quantum field theory

Can anyone refer me to some sources on generalizations of Bell's inequalities to quantum field theory (as opposed to quantum mechanics)? Scalar fields would be enough.
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164 views

Interpretation of an “interaction” term

In QFT a polynomial (of degree >2) in the fields is said to be an interaction term, Ex.: $\lambda\phi^4$. Question Is it possible to give an interpretation to terms like $\frac{1}{\phi^n}$? (for ...
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1answer
418 views

How to tell local and non-local in QFT?

I'm taking QFT course in this term. I'm quite curious that in QFT by which part of the mathematical expression can we tell a quantity or a theory is local or non-local?
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910 views

What is the role of the vacuum expectation value in symmetry breaking and the generation of mass?

Consider a theory of one complex scalar field with the following Lagrangian. $$ \mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\mu ^2\phi ^*\phi -\frac{\lambda}{2}(\phi ^*\phi )^2. $$ The ...
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308 views

Energy spectrum of a Dirac electron

How do you explain easily "The spectrum of an electron in a repulsive potential " and hence "bound state of charge conjugation" in Dirac hole theory ?
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165 views

Wilson lines, boundary conditions, surface defects of TQFTs

I asked the following question in mathematics stack exchange but I'd like to have answers from physicists too; I have been studying (extended) topological quantum field theories (in short TQFTs) from ...
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1answer
333 views

How does the dressed Klein-Gordon propagator look in position space?

The free Klein-Gordon propagator in momentum space $\sim (p^2-m^2+i\epsilon)^{-1}$ has just a single pole at $p^2=m^2$. The passage to Fourier space is difficult but possible. The result is very ...
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501 views

What is the hierarchy problem?

BACKGROUND So far I understood that the hierarchy problem was the large difference between the gravitational scale, $M_{pl}\sim 10^{18}\; [GeV]$, compared with the electroweak scale, $M_{ew}\sim ...
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1answer
165 views

Origin of Higgs ghosts

In M. Veltman's Diagrammatica, appendix E, one can find the full Standard Model lagrangian. Some sectors (e.g fermion-Higgs and weak sectors) contain so-called Higgs ghosts $\phi^+,\phi^-$ and ...
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1answer
230 views

Taylor series for unitary operator in Weinberg

On page 54 of Weinberg's QFT I, he says that an element $T(\theta)$ of a connected Lie group can be represented by a unitary operator $U(T(\theta))$ acting on the physical Hilbert space. Near the ...
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1answer
152 views

Relation between electric charge and gauge parameter of the moduli space of monopoles

I am studying about the moduli space of a 2 monopole system from Harvey's notes, and Manton's paper. In both of these, (Harvey section 6.2), after constructing the Lagrangian for a two dyons system, ...
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660 views

Dirac equation as Hamiltonian system

Let us consider Dirac equation $$(i\gamma^\mu\partial_\mu -m)\psi ~=~0$$ as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that ...
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3answers
337 views

Extending General Relativity with Kahler Manifolds?

Standard general relativity is based on Riemannian manifolds. However, the simplest extension of Riemannian manifolds seems to be Kahler manifolds, which have a complex (hermitian) structure, a ...
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2answers
170 views

Could we get rid of explicit fields derivatives in Quantum Field Theories?

For instance, if we choose the following scalar field Lagrangian, which is (I hope) Lorentz-invariant, where $l$ is a a length scale, and with a $(-1,1,1,1)$ metric: $$ \mathfrak{L}(x) \sim ...
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1answer
599 views

A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)

I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
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1answer
667 views

Charge conjugation in Dirac equation

I need to know the mathematical argument that how the relation is true $(C^{-1})^T\gamma ^ \mu C^T = - \gamma ^{\mu T} $ . Where $C$ is defined by $U=C \gamma^0$ ; $U$= non singular matrix , $T$= ...
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4answers
423 views

Translations of field operators in QFT

A question in the book QFT of Srednicki: This concerns the relativistic QFT generalization $$\tag{2.21} {{e}^{-i\hat{P}x/\hbar}}\psi (0){{e}^{i\hat{P}x/\hbar}}~=~\psi (x)$$ of the formula ...
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496 views

Renormalization of field strength

I'm revisiting the elementary algorithms of renormalization that are taught in a classroom setting and find that the procedure taught to students is as follows: Write down the bare Lagrangian: ...
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1answer
424 views

Chiral anomaly in odd spacetime dimensions

In odd number of space-time dimensions, the Fermions are not reducible (i.e. do not have left-chiral and right-chiral counterparts). Does this mean that there is no such thing as 'chiral' anomalies ...
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1answer
253 views

Why can you re-write the functional measure of a real-valued field $\phi(x)$ as $\mathcal{D}\phi=\prod_{k_n^0>0}dRe \phi(k_n) d Im \phi(k_n)$?

This happens in Peskin and Schroeder, An Introduction to QFT, on page 285. They set out to calculate correlation functions for the free real-valued Klein-Gordon field $\phi(x)\in \mathbb{R}$. They ...
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1answer
389 views

Ward Identity makes QED logarithmic divergent?

Quick question regarding superficial degrees of freedom and Ward identities. For instance in Peskin and Schroeder it is stated that the photon-self energy is superficially quadratically UV divergent ...
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4answers
754 views

Uncertainty Principle for Information?

I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question: While we have Heisenberg uncertainty principle on measuring coupled observables, ...
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122 views

Naive Uncertainty principle for string theory

Is it possible, in some sense, that a naive uncertainly principle for string theory could be expressed as : $$ \Delta x_i \Delta p_j \Delta \sigma ~=~ \delta_{ij} \hbar \ell_s$$ where $\ell_s$ is ...
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1answer
208 views

Why does renormalization need an unbroken symmetry?

Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
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353 views

Kugo and Ojima's Canonical Formulation of Yang-Mills using BRST

I am trying to study the canonical formulation of Yang-Mills theories so that I have direct access to the $n$-particle of the theory (i.e. the Hilbert Space). To that end, I am following Kugo and ...
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246 views

Is single photon annihination of electron-positron pair prohibited by Feynman diagram analysis?

It is obvious that electron-positron pair cannot annihilate to a single photon which will violate the momentum conservation. My question is can we get this knowledge from Feynman diagram or ...
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1answer
339 views

Speed of light and virtual particles

After becoming extremely bored while studying for an Afrikaans exam, I started thinking about virtual particles. So, can light (photons) interact with virtual particles (even though they only exist ...