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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Equivalence principle for test fields

My question is very simple. We all know that, for a test particle(classical) in a gravitational field, the motion is only determined by the geodesic lines(let's forget about the initial conditions for ...
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57 views

Does a charged particle propagating in free space have a 'self-energy' like term due to it’s interaction with the fluctuations of the quantum vacuum? [on hold]

Does a charged particle propagating in free space have a 'self-energy' like term due to it’s interaction with the fluctuations of the quantum vacuum? (particle-antiparticle pairs popping into and out ...
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2answers
89 views

Why Kink can not tunnel to vacuum, and is topologically stable?

Why the kink $$\phi(x)=v\tanh(\frac{x}{\xi}) ,$$ can not tunnel into vacuum $+v$ or $-v$ (Spontaneous symmetry breaking vacuum). From the boundary condition ($x\rightarrow \pm\infty, ...
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1answer
73 views

Derivation of eq 6.17, Peskin and Schroeder

I am having trouble following a derivation in Peskin and Schroeder's textbook, namely equation 6.17 on page 182. It seems benign at first, but I am completely stuck. Essentially, we have an expression ...
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23 views

Holography with wave functionals rather than partition functions

Roughly speaking Gubser-Klebanov-Polyakov Witten's (GKPW) prescription in the context of holography tells us partition function of CFT is "equal" to that of the gravity theory in one higher dimension ...
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64 views

Why is gravity sensitive to absolute energies?

In QFT absolute energies play no role in the physical set-up, only relative energies (i.e. energy differences) are important. However, in general relativity this doesn't appear to be the case, I've ...
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15 views

Bound states and corresponding elementary fields

Let's have some bound state, like positronium or meson. I need to calculate an amplitude of process which involves bound state in in- or out-state. Is it necessary to introduce corresponding ...
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244 views

Momentum Space Renormalization of $\phi ^6 $ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d $ for the energy functional: $$ f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2 $$ where $\ d$ is the dimension ...
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62 views

Why is the effective action $\Gamma[\phi_c] \propto -(VT)$ (spacetime volume)?

I'm asking about equation $(11.50)$ in Peskin and Schroeder where they state that the effective action evaluated at the classical field is given by $$\tag{11.50}\Gamma[\phi_c] = -(VT)\cdot ...
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2answers
308 views

$t\bar{t}$ asymmetry

Some weeks ago, there was lots of talk about this CDF paper: Evidence for a Mass Dependent Forward-Backward Asymmetry in Top Quark Pair Production where they measured a much higher asymmetry than ...
3
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1answer
35 views

One-point function and VEV in $\phi^4$-theory

Why is it that the one-point function in the $\phi^4-$theory, for example calculated from the generating functional, always gives zero value in absence of external source i.e., $J=0$? If there is ...
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36 views

How can the VEV of a field be a function of spacetime?

Often in the discussion of effective action and effective potential (say, in the context of $\phi^4-$theory )the one-point function in presence of source is defined as \begin{equation} \frac{\delta ...
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44 views

Riemannian generalization of Weierstrass transform

As it has been written on this Wikipedia page, one can define the Weierstrass transform on any Riemannian manifold. Even though, I couldn't find any references guess that the Weierstrass transform on ...
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4answers
996 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 ...
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1answer
131 views

Proper way to quantize the string in the light-cone gauge

In many books like Polchinski and Green-Schwarz-Witten the light cone quantization is carried out in a fast way. They just use the virasoro constraint in the light-cone gauge to get the ligh-cone ...
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66 views

Derivation of the Lorentz algebra explicity [closed]

I need the complete proof for commutation relation of the Lorentz group generators. The proof of Lorentz algebra using this commutation relation.
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107 views

Singlet neutrinos decaying to Higgs bosons during leptogenesis

(i) The Lagrangian of electroweak model extended with right-chiral singlet neutrinos $N_{iR}$ contains the Yukawa coupling term+ the bare Majorana mass term $$f_{\alpha ...
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1answer
100 views

Path Integral Evaluation

I've seen the path integral formulation now in a couple contexts (propagator in quantum mechanics, and coherent state functional integral in many body physics). I'm now struggling with how to actually ...
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29 views

Can we have supersymmetry using real scalar instead of complex scalars?

I am aware that a suersymmetric theories containing a complex scalar a Weyl fermion and an auxiliary field exist. I was wondering if we can have something analogous using real and not complex scalar ...
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1answer
293 views

Fierz identity for Weyl spinors in tensor currents

Using Fierz identity I found that certain four-fermion operator with left $l_i$ and right-chiral $r_i$ Weyl spinors vanish $\bar{l}_1\sigma_{\mu\nu} r_2 \bar{r}_3 \sigma^{\mu\nu} l_4 =$ $ ...
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26 views

Path integral for boson vs fermion (soft derivation + use )

I have been looking around for a soft derivation with a bit of detail for boson and fermion path integrals that I could understand. I have a passing knowledge generally of what a path integral is in ...
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2answers
68 views

Self-teaching Green's function approach to quantum many-body systems

My question is where can I find a good book, review, online course, or all of them for self-teaching Green's function in quantum many-body problems (if it has problems with solutions for ...
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46 views

Effect of orbifolding on form ields

A paper by Lalak et al, entitled "Soliton Solutions of M-theory on an orbifold", considers the brane solutions of 11 dimensional supergravity on a space of the form $R^{10} \times S^1/\mathbb{Z}_2$. ...
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1answer
80 views

Why cannot massless particles carry charges? [duplicate]

How to show that massless particles do not carry charges from QFT's point of view?
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56 views

Multiplying propagators

The amplitude for a particle going from $x$ to $y$ is $G(x,y)$. So why isn't the amplitude for going $x$ to $y$ to $z$ $$ G(x,z) \neq \int G(x,y)G(y,z) dy^4 $$ but instead $$ G(x,z) = \int ...
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38 views

Unitarily Inequivalent Representations

The definition of unitarily equivalent representations I am using is the one given here: https://en.wikipedia.org/wiki/Haag%27s_theorem. Now in this text ...
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224 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 ...
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29 views

How should we deal with diagrams which do not conserve particle number in a non-relativistic field theory?

In the last 10 years there has been more and more crossover of techniques from high energy physics being used in AMO and condensed matter scenarios, in particular diagrammatic techniques and related ...
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38 views

Bound state of $\mu^- \mu^+$ . Why non-relativistic muon states?

Peskin & Schroeber page 148 discuss the creation of a $ \mu^+ \mu^-$ resonance state . Equation (5.44) describes the creation of a Spin Up bound $ \mu^+ \mu^-$: $$ \mathcal{M} = \sqrt{2M} \int ...
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1answer
765 views

Could this model have soliton solutions?

We consider a theory described by the Lagrangian, $$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$ The corresponding field equations are, ...
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1answer
31 views

Regarding different representations of the Lorentz Group & its defining properties

Take $\Lambda$ to be a Lorentz matrix, it satisfying $\Lambda^T \eta \Lambda=\eta$. By writing $\Lambda=\exp[-\frac{i}{2}\omega_{\mu\nu}\mathcal J^{\mu\nu}]$, we find that the generators satisfy $$ ...
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19 views

Is one of the matrix elements in the optical theorem complex conjugated or not?

The standard form of the optical theorem for amplitudes (Edit: in D-dimensional space-time) looks like this: \begin{align*} -i& (\mathcal{M}(in \rightarrow out)-\mathcal{M}^*(out\rightarrow in))\\ ...
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2answers
43 views

Time-ordering and Dyson series

In Dyson series we use a time-ordered exponential by arguing that a Hamiltonian at two different instants of time does not commute. Why is it that so? Can anyone explain with example why should the ...
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1answer
55 views

Is microcausality a statement about locality?

As far as I understand it locality is the rejection of action-at-a-distance. By this I mean that in a given frame of reference at a given instant of time (in that reference frame), two physical ...
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3answers
152 views

What role does “spontaneously symmetry breaking” played in the “Higgs Mechanism”?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
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43 views

Do quantum fluctuation particles have any trend regarding their average velocity and direction? If so does that infer and inherent reference frame?

In a vacuum particles appear from no where due to quantum fluctuations. In various reference frames would the overall mass of all these particles be moving in a direction? Could I find a reference ...
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1answer
84 views

Is there a reason why a relativistic quantum theory of a single fermion exists, but of a single scalar not?

When we try to construct the relativistic generalization of non-relativistic time dependent Schroedinger equation, there are at least two possible completions - Klein-Gordon equation and Dirac ...
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35 views

Normalising a massive propagator?

If you take a propagator Greens function for a massless photon from the origin as $$G(0,x) = \frac{1}{x^2-t^2 +i \varepsilon}$$ then the normalisation factor at time t is: $$ N = \int |G(0,x)|^2 ...
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1answer
46 views

Issues with the chain rule in derivatives in chiral perturbation theory [duplicate]

I realize that this is a purely math question, which however has arisen in a physics computation. The reason to post it here is that I want a fast dirty answer. Not something cluttered with ...
4
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1answer
92 views

Anomaly cancellation in the standard model (calculating the symmetrized trace of generators)

The Problem We can show that the condition for the Standard Model to be anomaly-free is that the symmetrized trace over the generators of the gauge group vanishes: \begin{align} \text{tr} ...
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2answers
205 views

Massless boson in 2D and its (retarded) propagator

I have the retarded propagator for a free scalar field in 1+1 dimensions. Inside the light cone, this looks like $J_0(m \sqrt(t^2-x^2))$, $J$ being a Bessel function. When I take the massless limit, ...
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1answer
241 views
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24 views

Experimental sensitivity to variance of the fine-structure constant

If some of the fundamental parameters of the Standard Model had quantum uncertainties, they should manifest mainly as a minimum width in the experimental sensitivity of measurement of some of them, ...
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96 views

The classification of particles or fields in general spacetime- Is it still meaningful to say spin-0, 1/2 ,1 field in general spacetime? [closed]

In 3+1 dim Minkovski spacetime, the classification of particle or field, that is spin-0, 1/2 , 1..., depends on the representation of the universal covering group of $SO(1,3)$, that is $SL(2,C)$. When ...
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1answer
272 views

QFT question, scalar field and so on

$\newcommand{\bbraket}[3]{\langle #1 | #2 | #3 \rangle} \newcommand{\ket}[1]{|#1\rangle} \newcommand{\bra}[1]{\langle #1 |}$ I have such a problem with a proof. I'm studying the two point correlation ...
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1answer
158 views

Quantizing highly nonlinear field-theories?

I'm wondering how to go about quantizing a classical field theory which looks nothing like a free field theory plus a perturbation term. Suppose for concreteness I have the classical hamiltonian $ ...
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1answer
133 views

Is $SU(2)$ really broken by the Higgs VEV or just hidden?

It's generally stated in the textbooks that whent the Higgs field acquires a certain vev the corresponding symmetry is spontaneously broken. For example in A. Zee - QFT in a Nutshell: But none of ...
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2k views

What is the fundamental reason of the fermion doubling?

Recall that the fermion doubling is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds ...
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61 views

Taking squares or square roots of differential forms?

Reading the recent paper Loop Integrands from the Riemann Sphere by Yvonne Geyer, Lionel Mason, Ricardo Monteiro and Piotr Tourkine I noticed that the authors occasionally seem to take squares and ...
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1answer
347 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...