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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Why the heat capacity doesn't diverge in the Kosterlitz-Thouless (KT) phase transition?

The KT transition has a special properties that, during the phase transition the heat capacity stay finite (so the behaviour of the heat capacity cannot reflect any critical behaviours). However, the ...
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207 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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43 views

What is primitive divergence?

As in the title, what is primitive divergence? How is it distinguished from normal divergence? As a followup, what is a primitive divergent graph in a theory? Some simple examples?
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304 views

Determinant for a coupled fluctuation Lagrangian

Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
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59 views

Two creation operators acting on a state

If $a_p^\dagger$ is the creation operator for an electron with momentum $p$ and $b_q^\dagger$ is the creation operator for a positron with momentum $q$, what does $a_p^\dagger b_q^\dagger \left| 0 ...
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82 views

How many particles in $\phi_0(x)^2|0\rangle$?

In Schwartz's "QFT and the standard model" on pg 22 he writes: A two or zero particle state as in $\phi_0(x)^2\left|0\right>$. I was wondering how this can be proved? I tried checking if ...
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74 views

Weinberg-Witten theorem and Landau pseudotensor, or how QFT can make prediction about GR

Weinberg-Witten theorem states that there isn't Poincare covariant stress-energy tensor for massless fields with helicity more than $1$. The only example of such higher helicity field is graviton. ...
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142 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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88 views

Basic doubt on the philosophy of Quantum field theory and General relativity

As I understand, the basic idea of General relativity is that the 4-d spacetime is "deformed" because of the presence of matter-energy, in other words no pre-existing (or background) space is assumed ...
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134 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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52 views

Understanding Fierz rearrangement identity

I'm trying to get a better grasp of the Fierz rearrangement identity for 2-component spinors (Equation 2.20 I'll be using the Van der Waerden notionation used in the given link) $$ \chi_\alpha (\xi ...
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54 views

“No-go” theorems and goldstone bosons

There are "no-go" theorems who forbid interaction through soft helicity 3 and higher massless particles and soft interaction between massless fermions with spin more than $\frac{3}{2}$. But if ...
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34 views

Why only the spin $j=\frac{1}{2}$ has relativistic wave function equation that conserves positive probability?

The Dirac wave function can be thought as a relativistic wave equation, where the solution has a positive definite norm. I know that this same equation can't be thought so seriously as a wave equation ...
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159 views

effective field theory of the projective semion model

The "projective semion" model was considered in http://arxiv.org/abs/1403.6491 (page 2). It is a symmetry enriched topological (SET) phase. There is one non-trivial anyon, a semion $s$ which induces a ...
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521 views

Teach me Wick's theorem the honest way

Generally speaking the average guy marginally acquainted with quantum field theory or advanced combinatorics describes Wick's theorem as some sort of correspondence between higher order differential ...
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29 views

Mass correction to a massless boson

Suppose I have a boson and a fermion: $$ \mathcal L = -\frac{1}{2}(\partial \phi)^2 -m_\phi^2\phi^2 - \bar \psi \not \partial \psi - m_\psi \bar \psi \psi + \lambda \phi \bar \psi \psi $$ In the ...
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28 views

What exactly is Weinberg's power counting theorem?

The massive gravity propagator goes like $\sim \frac{p^2}{m^4}$ at high energies and in this case we cannot apply Weinberg's standard power counting arguments. I have read something like that ...
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31 views

Higher spins elementary particles

Lorentz invariance requirement of theory imposes the absense of interactions between spin 3 and higher spins bosons and arbitrary field (like spin $\frac{1}{2}$ fermions etc) at least in infrared ...
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24 views

Isotopic invariance

I am reading something related to Isotopic invariance. As i have read, Isotopic invariance of the interaction between nucleons (proton and nucleon) is just approximate since masses of proton and ...
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660 views

What do the four components of Dirac Spinors represent in the Standard Model?

I've been trying to get my head around the formalisms used in the Standard Model. From what i've gathered Dirac Spinors are 4 component objects designed to be operated on by Lorentz Transformations ...
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1k views

Equation of everything

Is this equation in the image true? Can you give some topics that I can cover the equation? Similar equation from http://www.preposterousuniverse.com:
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95 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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105 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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106 views

Poincaré' lemma and EM potential $A^{\mu}$

My lecturer said that given the sourceless Maxwell's equations $$ \partial_{\mu}\, ^ *F^{\mu\nu} = 0 $$, we can find a solution $$ F^{\mu\nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu},$$ that ...
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36 views

Multiparticle Mandlestam Variables Extension

So in 4D we have three Mandlestam variables for a 4-particle scattering process. This corresponds to $p_i^\mu$ giving us 16 degrees of freedom. Momentum conservation reduces this by 4, and we have 4 ...
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32 views

Fermion - Antifermion (annihilation) scattering amplitude

I'm trying to get the scattering of the diagrams described here in the "annihilation, part ii" (fermion/antifermion - scalar/scalar) ...
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262 views

Motivation to introduce von Neumann algebras in addition to $C^*$algebras?

Observables are self-adjoint elements of a $C^*$algebra. As such, this structure seems sufficient to describe physics. A theorem by Gelfand and Naimark says that a $C^*$algebra can always be ...
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163 views

Why are right hand neutrinos unaffected by all forces except gravity

I'm curious as to something I read on Berkeley's website. Does anyone happen to know why, according to this model,right hand neutrinos are unaffected by all forces except gravity? (Model taken from ...
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497 views

Quantum to classical mapping: quantum criticality and path integral Monte Carlo

I'm trying to understand the connections between quantum models in d dimensions and classical models in (d+1) dimensions within two, possibly related, contexts: (i) in path integral monte carlo, the ...
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148 views

Fock representation of a electromagnetic wave

Suppose an arbitrary classical (electromagnetic) wave package $E(x)$. What is its Fock space representation? I.e. I am looking for a state $| \psi \rangle$ such that $\langle \psi | \hat E(x) | \psi ...
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50 views

Supermultiplet dimensions from Young Tableaus

In John Terning's book, on pages 14 and 15, there are lists of $\mathcal{N} = 2$ and $\mathcal{N} = 4$ supermultiplets, labeled in terms of the dimensions of the corresponding R-symmetry $d_R$ and ...
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158 views

Photon polarization sum prescription in $e^-e^+\to{}2\gamma$

In calculating the amplitude for the process $e^-\gamma\to{}e^-\gamma$ the substitution $\sum\epsilon_{\mu}\epsilon^*_{\nu}\to-\eta_{\mu\nu}$ is useful to sum over photon polarizations. If we ...
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Virtual particles, electrons and quantum foam [duplicate]

Do quantum foam, electrons and virtual particles pop in and out of existence without a cause? If so, aren't they violating the laws of cause and effect and the 1st law of thermodynamics? is the 1st ...
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30 views

Virtual Particles and Causation [duplicate]

Sometimes when people debate what type of cause a universe with a beginning may have Virtual Particles has been used as an example of a thing that can arise without a cause. So my question would be ...
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1answer
120 views

What's the difference between correlation functions and S-matrix, and between in-in formalism (or “closed time path formalism”) and in-out formalism?

I was reading the "in-in" formalism (or "closed time path formalism" used in condensed matter physics) in cosmology created by Schwinger in 1961, and there is a saying: "they care about correlation ...
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1answer
87 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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Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
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1answer
296 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 ...
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1answer
61 views

Pauli Villars Regularization

Consider the t-channel diagram of phi-4 one loop diagrams. Evaluated it is, with loop momenta p, $\frac{\lambda^2}{2}\displaystyle\int\frac{d^4p}{(2\pi)^4}\frac{1}{(p+q)^2-m^2}\frac{1}{p^2-m^2}$ If ...
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1answer
43 views

Renormalization Using Momentum Cut-off Regularization, What Are The Subtraction Schemes Used?

In most of the books on QFT, the author talks about various methods of regularization but in the end chooses the dimensional regularization and MS-bar scheme when discussing the final renormalization, ...
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106 views

Does regularity of distributions have anything to do with definiteness of their product?

Recently I've gone through some literature concerning causal perturbation theory (CPT). As is well known, it deals with UV divergences in QFT by defining products of (operator-valued) distributions ...
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426 views

Green's function for the inhomogenous Klein-Gordon equation

I'm trying to solve the massive Klein-Gordon equation in good old Minkowski space-time: $$(\square + m^2) \phi = \rho(t,\mathbf{x})$$ where $\square = \partial_{\mu} \partial^{\mu} = \partial_{t}^2 - ...
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226 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
251 views

Can you take the cutoff to infinity at a conformal fixed point?

A conformal fixed point is defined by $$\beta(g)=0$$ We hence know that couplings, masses and dimensions of operators do not flow in the effective Lagrangian when we change the renormalization ...
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4answers
98 views

Importance of local conservation of probability

In almost every textbook of quantum mechanics we can find the derivation of the local conservation of probability. $$\nabla\cdot\vec{J}+\partial_t (\psi^*\psi)=0$$ where $\vec{J}$ is probabilty ...
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273 views

Calculating $\mathrm{Tr}[\log \Delta_F]$

I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this question), which looks like $$ \widetilde\Delta_F(p) = ...
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659 views

Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
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1k views

Energy conservation limited by uncertainty principle

The way I learned it from practicing Fourier analysis and signal processing besides quantum mechanics, is that Energy conservation cannot be achieved in short time scales, and that limits energy ...
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930 views

How Uncertainty Principle, Vacumm 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 Furrier transforms in QFT we should have an analogue to the usual Heisenberg ...