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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Integration by parts

Zee in his book, Quantum field in a nutshell mentioned the following, p. 22: Equation (14): $$Z=\int{D\phi}e^{i\int d^4x{ {\frac{1}{2}[(\partial \phi)^2-m^2\phi^2]+J\phi}} }$$ He said then, ...
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36 views

How is $\varepsilon_+^\mu(p) = \bar{v}(k) \gamma^\mu u(p)$ derived?

The relation $$\varepsilon_+^\mu(p) = \bar{v}(k) \gamma^\mu u(p)$$ is sometimes used to ease calculations of Feynman amplitudes with external gluons (see for example here at (2.13)). Where does this ...
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77 views

What is the physical meaning of anti-commutator in quantum mechanics?

I gained a lot of physical intuition about commutators by reading this topic. What is the physical meaning of commutators in quantum mechanics? I have similar questions about the anti-commutators. ...
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13 views

Conductivity Matrix (Symmetry Information)

I'm trying to understand the symmetry content of the conductivity matrix: one information is, presence of time-reversal symmetry causes the off-diagonal terms to vanish. When this is broken (e.g. in ...
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38 views

Coupling of matter field with gauge boson and Goldstone boson:

What's the fundamental difference between the way a gauge boson gets coupled to a matter field, preferably a Fermionic field and the way a Goldstone boson gets coupled to the matter field ? In ...
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197 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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25 views

Charge Conjugation Operator in Supermultiplet

Consider an $\mathcal{N}=1$ left-handed chiral supermultiplet. The particle content is $$L = (\phi\quad e_L) $$ where $\phi$ is a complex scalar and $e_L$ a left handed Weyl fermion. People usually ...
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Gauge choice after Spontaneous Symmetry Breaking

After the spontaneous breakdown of local symmetry in presence of gauge fields (Higgs Mechanism), we can always choose a gauge where the Goldstone bosons are eaten up by the gauge field (also called ...
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Leptons slide between quarks? [on hold]

I wonder if one of particles (maybe quarks?) are constructors of highways in 3d field for others floating around re/distributing energy by some (leptons?), restricted to laws set by (bosons?). If ...
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20 views

Uncharged Gluon Representation

I'm currently learning for an exam and in an old exam the question was posed: If Gluons were uncharged, under which representation would they transform? The ...
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53 views

Two different transformation laws for Quantum Fields

I found a nice answer to a problem that was bothering me for quite a while in a lecture script (unfortunately in german). The first step of the answer, is what remains unclear to me. The script states ...
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Supersymmetric Extension of Mirror Model

A brief description of Mirror Matter can be seen. Some papers about Mirror Matter : Berezhiani, Kolb, Seckel, Turner, Foot,Lew,Volkas Does anyone have some references about How to construct ...
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49 views

How to compute the normal ordered angular momentum of a Klein-Gordon real scalar in terms of ladder operators?

I'm trying to compute the angular momentum $$Q_i=-2\epsilon_{ijk}\int{d^3x}\,x^kT^{0j}\tag{1}$$ where ...
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217 views

Position operator in QFT

My Professor in QFT did a move which I cannot follow: Given the state $$\hat\phi|0\rangle = \int \frac{d^3p}{(2\pi)^3 2 E_p} a^\dagger_p e^{- i p_\mu x^\mu}|0\rangle,$$ he wanted to show that this ...
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15 views

Dalitz plot for $ \pi \to \gamma (1) + e^+ (2) + e^- (3) $

I am studying the decay above and I need an exact form of Dalitz plot in coordinates $m^2_{12}, m^2_{23}$ to integrate over three-particle phase-volume. Please, tell where to read about it? I tried ...
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210 views

What is the Quantum Transition Time for Photon Emission?

When an electron in an atom changes energy states to emit a photon, how long does the process take? Is this question even meaningful?
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67 views

Normal Ordering the phi^4 interaction

I am trying to quantize the quartic potential $\frac{\lambda}{4!}\phi^{4}$ in a box of side length $L$, with periodic boundary conditions. I have expanded the field ...
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1answer
34 views

How to see the ground state degeneracy (GSD) from a $BF$ theory in $2+1$ $d$?

I have seen many times the $BF$ theory has non-trivial ground state degeneracy (typically on torus), but I can not see how the conclusion come out. Recently I found a paper by Hansson, Oganesyan and ...
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78 views

Why do we believe in a “force” driven universe? [on hold]

Why do we not believe in the potential for a "unified force field" universe, to the exclusion of the belief in the potential for a mechanical, gear driven universe, if the correct shape for the gear ...
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37 views

Temperature in CFT

Non-vanishing Temperature can break conformal symmetry(Can anyone show this point explicitly), my question is that in AdS/CFT the temperature of boundary field theory is non-zero, why the boundary ...
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60 views

Schrodinger Wave Functional (quantum fields) - Solving Functional Gaussian Integrals

Okay, So i'm doing some research that involves the Schrodinger representation in quantum field theory. The ground state wave functional for the Klein Gordon field is a generalized gaussian in position ...
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2answers
54 views

Non-invariance of the Interaction term in QED lagrangian

The interaction term in the QED Lagrangian $$\mathcal{L}_{int}=e\bar\psi\gamma^\mu A_\mu\psi$$ changes under a gauge transformation $$A_\mu\rightarrow A_\mu+\partial_\mu\chi$$ Doesn’t it affect the ...
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Is there some special case where a fermion can mediate a force?

Looking at the comments of this questions Does the gravitino contribute to the gravitational interaction? and even considering that the answers here in this other question Why are all force particles ...
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68 views

How Should I Think About the Dirac Equation?

In Weinberg's QFT Vol. 1 he says the Dirac equation is not a true generalization of Schrodinger's equation, that it does not stand up to inspection when viewed in this light. He says it should be ...
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40 views

In SUSY, why do fermions and gauge bosons in the same multiplet both transform in the adjoint representation of the gauge group?

I'm trying to understand a certain point about supersymmetry. We are dealing with a N=1 (i.e, one supersymmetric flavour), massless, four dimensional theory. Then the vector multiplet consists of a ...
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45 views

Time evolution operator of a periodic Hamiltonian

Suppose we have a Hamiltonian $H(t)$ with periodicity $T$. The time evolution operator in a full period is $$U_1=\cal{T}e^{-i\int_0^T H(t)\mathrm{d}t}$$, where $\cal{T}$ is time ordering operator; ...
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96 views

How to understand “always create before we annihilate, not the other way around”?

On the book QFT in a Nutshell by A.Zee page 61 writes Always create before we annihilate, not the other way around. —Anonymous But in this Phys.SE question we are doing it the other way ...
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70 views

Non-Perturbative feynman diagrams?

The wikipedia page for Feynman Diagrams claims that Thinking of Feynman diagrams as a perturbation series, nonperturbative effects like tunneling do not show up, because any effect that goes to ...
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55 views

Baryon in terms of quark fields

What is the most general way to write down a current describing a baryon made from quarks $\psi_i^\alpha$? Let's say we suppress flavour indices but want to write colour $(i,j)$ as well as spinor ...
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46 views

How to construct singlet and other multiplets from two triplets

Let an $SU(2)$ isotriplet operator is given by\begin{equation}\bar{l^c}i\tau_2\vec \tau l=l^T Ci\tau_2\vec \tau l\sim 3\end{equation} and an isotriplet Higgs field \begin{equation}\vec \Delta\sim ...
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1answer
68 views

Are the Yang-Mills equation and its generalization gauge invariant?

I have derived the Yang-Mills equation and its generalization coupled to a current of a scalar field $\phi$ by extremalizing the action describing a $\mathrm{SU}(2)$ scalar field gauge theory: ...
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43 views

Mixed two-point vertex in QFT

I am considering a theory with two fields, say $\phi$ and $\psi$. The Lagrangian contains quadratic terms, i.e., propagators for both fields and a quartic interaction term for one of the fields. ...
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30 views

Scalar Yukawa Theory in non-relativistic limit

I'm new to QFT, and am enrolled in a class at my school. I feel as though the teacher didn't give us the tools to tackle this problem yet. It's only the second week and we've gone through at most ...
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39 views

What is the central charge about? [closed]

I have two very basic questions. What is meant by the term conformal field theory? What is the central charge in a conformal field theory?
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61 views

New Supersymmetry Algebra

We know that SUSY generators commute with translation $$ [P_\mu,Q_\alpha]=0 $$ I have some questions: What is this equation physical meaning? Is it possible to make "SUSY-like" generators that do ...
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1answer
25 views

scattering by weak potential and the adiabatic hypothesis

In Ryder QFT, regarding the calculation of the scattering amplitude by a weak potential $V$, the potential is assumed to be switched on and off slowly using the adiabatic hypothesis. But there is a ...
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1answer
115 views

Is this summary of modern theoretical physics correct?

This is not exactly a physics question; it's more of a question about physics. You'll see what I mean in a minute. My understanding of modern theoretical physics is below. What I want to know is: Is ...
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14 views

Mean-field approach to quantum phase transitions in Fermi systems

I have a basic confusion concerning the mean-field theory of quantum phase transitions in Fermi systems. Consider as an example the BCS theory of superconductivity in a Dirac fermion system, ...
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1answer
62 views

Is it possible to make superpartner of Standard Model live in Mirror World?

In the ordinary Supersymmetry (SUSY), the superpartner of SM live in SM world (matter world). Then we introduce mirror world with mirror particle live there. I would like to make a new concept that ...
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42 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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63 views

Several Complex Variables in QFT

After reading the very interesting quote about several complex variables in QFT: "The axiomatization of quantum field theory consists in a number of general principles, the most important of ...
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1answer
112 views

How are Feynman rules derived (in general)?

There are some questions (not all answered) on how Feynman rules for specific cases are derived (e.g. Sign of Feynman rules with derivative couplings, Feynman rules for coupled systems, How can we ...
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1answer
97 views

Physics in torus, cylinder, Klein bottle and mobius strip

In string theory, or supersymmetric gauge theory, they often calculate the partition function on specific Riemann surfaces, such as torus, cylinder, Klein bottle, Mobius strip. Refer to the ...
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Are critical exponents below and above the critical point always same?

The scaling relations don't distinguish the the critical exponents below and above the critical value. In the mean field level, I understand these critical exponents are same whatever one approaches ...
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1answer
137 views

Why is Planck's constant the same for all particles?

This question came to me while reading "Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?". This question has a nice answer that explains that wave number has be ...
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46 views

Why is Quark Mixing forbidden in the Lagrangian (pre CKM)

The corresponding term in Lagrangian for the coupling of quarks to gauge fields reads $$ \sum_{i} \bar Q_i D_\mu \gamma^ \mu Q_i .$$ Considering the Yukawa terms it is generally stated, that no ...
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Retarded thermal Green function

I'm working with finite temperature field theory, but I'm having problems understanding the retarded Green's function in this formalism. I'm reading Niemi and Semenoff's article "Finite Temperature ...
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196 views

Why particle number operator $\hat{N}$ is $\hat{a}^\dagger\hat{a}$ rather than $\hat{a}\hat{a}^\dagger$?

Both $\hat{a}^\dagger\hat{a}$ and $\hat{a}\hat{a}^\dagger$ are Hermitian, how do we know which one represents the particle number?
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Integration & bremsstrahlung calculation

In this paper (relevant pdf section) that I'm reading, involving the calculation of bremsstrahlung in electron proton scattering (diagram below), the author calculates the integral over outgoing ...
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Split property for type III algebras entails practical separability

I am reading Halvorson's thesis (http://philsci-archive.pitt.edu/346/1/main-new.pdf), however I don't understand a proof at p.50 where he tries to explain why the split property allows a local agent ...