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 a superfluid in field theoretic terms?

I'm wondering how one precisely defines a superfluid in terms of the effective field theory description. In Nicolis's paper http://arxiv.org/abs/1108.2513 there seems to be an extremely simple ...
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76 views

Field redefinitions and new counterterms

My question was motivated by my attempt to answer this question. Suppose we are given an action and we make a change of variables such that the theory is non-renormalizable. Does the new theory then ...
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238 views

Deriving Feynman rules from Renormalized Lagrangian

In the context of Renormalized Pertubation Theory Peskin Schröder says: The Lagrangian $$ \mathcal{L}=\frac{1}{2} (\partial_\mu\phi_r)^2-\frac{1}{2}m^2\phi_r^2-\frac{\lambda}{4!}\phi_r^4 + \frac{1}{2} ...
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246 views

Is the Higgs bare mass larger than the physical mass?

The Higgs boson propagator can be written $$\frac{1}{p^2-m^2+\Sigma(p^2)}$$. If we take $p^2=m_P^2$ the physical mass, we get $m_P^2=m^2-\Sigma(m_P^2)$. Now, if $\Sigma\sim \Lambda^2$, we get $m^2\sim\...
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630 views

Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
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401 views

Non abelian gauge theory with charged scalar field

Suppose we have an SU(N) non abelian gauge theory coupled with a multiplet of complex scalar fields $\Phi$. The lagrangian would be $$ L= - \frac 12 \text{Tr } F_{\mu\nu}F^{\mu\nu} + |D_\mu \Phi|^2 - ...
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117 views

d=2 O(3) sigma model becomes “conformal antiferromagnet”

In Advanced topic in quantum field theory / M. Shifman on page 251 the author discusses the fact that the theta term is topological and does not affect the equations of motion. Then he said: "In ...
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178 views

Finding difficulties in taking continuum limit in nonlinear sigma model

I am learning nonlinear sigma model from Assa Auerbach's book "Interacting Electrons and Quantum Magnetism" and getting some difficulties in taking continuum limit. I am following chapter 12: The ...
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161 views

Categorizing solutions to Hierarchy problem

We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
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335 views

Computing functional determinant for Dirac fermions

In the path integral formulation for quantum field theory, one often encounters functional determinants of operators, for example for a free scalar field $\log \det (\partial^2+m^2)$. For this ...
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107 views

Does the Standard Model plasma develop a spontaneous magnetisation at finite temperature?

Reference: arXiv:1204.3604v1 [hep-ph] Long-range magnetic fields in the ground state of the Standard Model plasma. Alexey Boyarsky, Oleg Ruchayskiy, Mikhail Shaposhnikov. The authors of this paper ...
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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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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 ...
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541 views

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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700 views

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? ...
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347 views

An use of the Schwinger-Dyson equation

I was confused as to how the equation 10 on page 7 or equation 21 on page 8 of this paper http://arxiv.org/abs/1211.1866 was derived. Can someone explain from where does this come and what do the "...
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163 views

Gauge-invariance of pole mass using Ward Identity

I am able to explicitly verify to one-loop order that pole masses are independent of the choice of gauge paramter. But how do I use the Ward-Identity/Taylor-Slavnov identity show that the position of ...
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275 views

Dual Resonance Model: Fermions

I am going through Ramond's 1971 paper Dual Theory for Free Fermions Phys Rev D3 10, 2415 where he first attempts to introduce fermions into the conventional dual resonance model. I get the 'gist' of ...
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132 views

R charge of the chiral multiplet in $2+1$ dimensions

These are two examples that I am puzzled by, One can see in this paper on page 16 that for ${\cal N} =2$ theory on $2+1$ the R-charge of the $\phi$ and the $\psi$ is determined to be $\frac{1}{2}$ ...
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187 views

What is the rate of B violation expected in the standard model during high energy collisions?

In a recent question Can colliders detect B violation? I asked about detecting B violation in collisions. Here I am interested in the theory aspect. (I asked both questions originally in the same ...
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248 views

Semiclassical QED and long-range interaction

I'm interested in the (very) low energy limit of quantum electrodynamics. I've seen that taking this limit does not yield Maxwell equations, but a quantum corrected non-linear version of them. If ...
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242 views

Breaking of Lorentz invariance

Thinking about the concept of symmetry breaking led me to the following question: Let's say that I have a theory described by a Lorentz invariant Lagrangian, and the true vacuum of the theory is not ...
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465 views

Stability of the vacuum state of interacting quantum fields

"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
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192 views

Is there precision experimental evidence for Furry's theorem — that only even degree VEVs are non-zero?

Is there precision experimental evidence for or contradicting Furry's theorem -- that only even degree VEVs are non-zero, specifically for the EM field?
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304 views

1-form formulation of quantized electromagnetism

In a perpetual round of reformulations, I've put quantized electromagnetism into a 1-form notation. I'm looking for references that do anything similar, both to avoid reinventing the wheel and perhaps ...
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77 views

The relation between anomalous dimensions and renormalization constants

I am trying to understand the general strategy and technical details of calculating $\beta$-function at higher orders. $\beta$-function is the anomalous dimension of the coupling constant and there is ...
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81 views

What type of fields are continuous spin representations?

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a ...
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137 views

Relation between Borchers class and the LSZ formula on S-matrix equivalence

It seems well known that different quantum fields can give rise to the same $S$-matrix. I know of two ways this is described. The first is through the Borchers class of relatively local fields, i.e. ...
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63 views

Adiabatic turning on of coupling constant in simulation of $\phi^4$ theories in the JLP algorithm

In the Quantum Algorithms for Quantum Field Theories by Jordan, Lee and Preskill they have devised an efficient algorithm to simulate $\phi^4$ theories. Given by the Lagrangian density $$\mathcal{L}(\...
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138 views

Why does analytic continuation as a regularization work at all?

The question is about why analytical continuation as a regularization scheme works at all, and whether there are some physical justifications. However, as this is a relatively general question, I ...
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111 views

Scalar QED, are there any scalar-fermion vertices in this theory?

Consider QED with an additional charged (complex) scalar field, $\phi$:$$\require{cancel} \mathcal{L} = -{1\over4} F^{\mu\nu} F_{\mu\nu} + (D^\mu \phi)^*(D_\mu \phi) - \mu^2 \phi^* \phi - \overline{\...
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116 views

Free probability in Physics

Recently I have started reading some materials on non-commutative probability. IN this area mathematicians sometimes consider quantum theory as a non-commutative version of classical probability, with ...
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556 views

Quantum fields from cluster-decomposition principle

I would like help proving Weinberg's claim (I've quoted him below) that quantum fields are an unavoidable consequence of merging particle-based quantum mechanics with both Lorentz invariance and the ...
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152 views

Conversion of results between cutoff regularization and dimensional regularization

Generally it would be expected that a renormalizable/physical quantum field theory (QFT) would be regularization independent. For this I would first fix my regularization scheme and then compute stuff....
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160 views

$d=2$ pole argument of quadratic divergences in Peskin & Schroeder's book

Q1: My question is, in the context of dimensional regularisation(DREG, in dimension $d$), why do they mention the absence of $d=2$ pole in the gauge theory cases[1], whereas the $d=2$ pole is not ...
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158 views

Help to understand vertex function

In Weinberg's book (the quantum theory of fields, volume 1, pag 446, equation (10.4.19) ) is stated that $\int \ dx \ dy \ dz \ exp(-i p x - ik y + i lz) \langle\Psi_0,T\{J^{\mu}(x)\Psi_n(y)\bar \...
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92 views

Hamiltonian Operator for nonrenormalizable Effective Field Theories?

Assuming we have a Effective Field Theory, for example a Real Scalar Field Theory, defined through a Lagrangian density of the form $\mathcal{L}_{eff} = \frac{1}{2}\partial_\mu\phi \partial^\mu\phi - ...
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114 views

Can you gauge a $U(1)_L$ symmetry?

I recently calculating the one loop correction for the propagator of a gauge boson, $\hspace{5cm}$ I assumed arbitrary left and right couplings, $ g _L $ and $ g _R $. I found that the one loop ...
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94 views

General relativity from helicity 2 massless field theory by using Deser's arguments

Recently I have discovered the method of constructing of GR from massless field with helicity 2 theory. It is considered here, in an article "Self-Interaction and Gauge Invariance" written by Deser S. ...
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64 views

Spin-dependence of the directionality of dipole radiation

I am interested in understanding how and whether the transformation properties of a (classical or quantum) field under rotations or boosts relate in a simple way to the directional dependence of the ...
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42 views

When does the correlator of a string of fields and the current vanish “sufficiently fast” at infinity and Ward's identity?

One consequence of the Ward identity (cf. Di Francesco et al) is that it means variation of correlators under infinitesimal transformation is zero. This can be seen by integrating the ward identity, ...
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69 views

Finite corrections to the Higgs mass in SUSY

I am worried here about specific supersymmetric scenarios in which an energy scale above the TeV is introduces. An example would be the Seesaw extension of the Minimal Supersymmetric Standard Model. ...
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103 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: $S[\phi,\sigma]=\int{d^4x[-\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2-\frac{1}{2}M^2\sigma^2-\...
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188 views

Could energy be stored into (not extracted from) the quantum zero point field (like a battery)?

In order to explain the question clearly, I will make a short introduction. In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to ...
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110 views

Is $\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}$ true for two different spin 1/2 fermions?

In the context of seesaw mechanism or Dirac and Majorana mass terms, one often see the following identity $$ \overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}. $$ Here, I am using 4 ...
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486 views

Is non-relativistic quantum field theory equivalent with quantum mechanics?

Related post Can we "trivialize" the equivalence between canonical quantization of fields and second quantization of particles? Some books of many-body physics, e.g. A.L.Fetter and J.D....
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239 views

How does the renormalization scale $\mu$ cancel in all finite observables?

In dimensional regularization, we must shift the dimensionless coupling $g$ by the renormalization scale $\mu$ (which has unit mass dimension): \begin{equation} g \rightarrow \mu^{4-d} g \tag{1} \end{...
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79 views

Equality of electric charges of all leptons

What does it precisely mean the often repeated statement that the electric charges of all leptons are the same. Let's consider QED with two leptons: electron and muon. The interaction part of the ...
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110 views

Some questions about the large-N Gross-Neveu-Yukawa model

Consider the following action with a fermionic field $\psi$ and a scalar field $\sigma$, $S = \int d^dx \{ -\bar{\psi}(\gamma^\mu \partial_\mu +\sigma )\psi + \Lambda^{d-4}[ \frac{(\partial_\mu \...
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222 views

What is the point of path integral for boson and fermion?

I am a beginner to study QFT and confused about path integral for boson or fermion. I have read about the path integral for single particle, and finished some problems. But I cannot understand the ...