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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How to know if the pseudoscalar Yukawa Lagrangian is invariant under chiral transformation?

The pseudo-scalar Yukawa theory Lagrangian is $$\mathcal{L}=\bar{\psi}(i\gamma ^\mu \partial_\mu - m)\psi -g\bar{\psi}i\gamma^5\phi\psi,$$ where $g$ is a coupling constant. How can I show it is ...
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70 views

Off-shell external line

In some QFT textbooks, an external line which is off mass shell also concerns us. But according to the motion equation, shouldn't the single external line be on the mass shell? Especially when we ...
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3answers
123 views

Spontaneous symmetry breaking to subspace not giving massless bosons

I'm currently trying to understand spontaneously broken in general and have stumbled upon a weird result which doesn't seem to correspond to my knowledge about broken gauge symmetries. Suppose we ...
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724 views

Why fermions have a first order (Dirac) equation and bosons a second order one?

Is there a deep reason for a fermion to have a first order equation in the derivative while the bosons have a second order one? Does this imply deep theoretical differences (like space phase dimesion ...
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191 views

Renormalizability of standard model

I'm wonder what precisely is meant by the renormalizability of the standard model. I can imagine two possibilities: The renormalizability of all of the interaction described by the Lagrangian before ...
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86 views

Baryon in terms of quark fields – spinor index structure

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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195 views

Vacuum to vacuum transition amplitude using functional integral

The vacuum to vacuum transition amplitude for a free particle with source $J$ is given by $$Z_0[J]=\int D\phi \mathrm{exp}\{-i\int [\frac{1}{2}\phi(\square +m^2-i\epsilon)\phi-\phi J]d^4x\}$$ Let ...
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151 views

Renormalization, integrating out high momenta Wilson way

In equation $(12.5)$ in Peskin and Schroeder, they write out the generating function but leave out all quadratic terms of the form $\phi\hat{\phi}$ arguing that they vanish since Fourier ...
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132 views

How does conservation of energy manifest itself quantum mechanically?

We know that classically, if we have some theory $\mathcal{L}$ such that the action $\int d^4 x \mathcal{L}$ is invariant under time translation, then we can use Noether's theorem to find that (the ...
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273 views

Number of gravitons launched by a proton

The wikipedia article http://en.wikipedia.org/wiki/Gauge_bosons describes how in QM exchanges of gauge bosons carry force, and describes how the graviton may also be a gauge boson. If the observable ...
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244 views

Mathematical motivation of OPE?

In Peskin & Schroeder (and also Cheng which I have skimmed through) they motivate the Operator Product Expansion with a lot of words. Is there any way to motivate it mathematically, e.g. Taylor ...
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1answer
87 views

Can the strings in string theory be thought of as troughs in a field?

I figure that string theory is a new breed of QFT which looks at fields in terms of a network of strings and also incorporates gravity into its module, however my question is that since elementary ...
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187 views

What does an excitation in a field mean?

The term "field excitation" is used a lot especially when I hear about the Higgs boson. However, I cannot find an explanation of what precisely that means. I have a few questions relating to this. ...
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176 views

breitenlohner freedman stability condition

I am looking for a simple way to derive the breitenlohner-freedman bound. Actually I can't understand why we have stability above the BF bound and instability below the BF bound,while both have ...
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47 views

Pair production and initial separation

I was looking at the wiki article on electron-positron pair production (http://en.wikipedia.org/wiki/Pair_production) and have a question. The article states that the photon energy needs to exceed ...
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163 views

What is the four-dimensional representation of the $SU(2)$ generators?

Recently, I have been learning about non-Abelian gauge field theory by myself. Thanks @ACuriousMind very much, as with his help, I have made some progress. I am trying to extend the Dirac field ...
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380 views

Switching from sum to integral

I'm specifically asking about an equation in An Introduction to Quantum Field Theory, by Peskin and Schroeder. Example from page 374: $$\mathrm{Tr} \log (\partial^2+m^2) = \sum_k \log(-k^2+m^2)$$ ...
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207 views

How is a photon measured?

If photons transmit the electromagnetic force, which is observable: the photon or the electron? Do we ever directly measure a photon, or do we only measure it's effect on electrons. For example ...
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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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123 views

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

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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55 views

Deconfinement at high T $\leftrightarrow$ spontaneous breaking of the center of the gauge group

I am reading Witten's "Anti-de Sitter Space, Thermal Phase Transitions, And Confinement In Gauge Theories" (see here), in which he connects the confinement-deconfinement transition in $\mathcal{N}=4$ ...
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339 views

Energy conservation of Virtual Particles - Quantum Fluctuation?

I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the ...
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1answer
123 views

Integration by parts [closed]

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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160 views

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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393 views

QED Vertex Factor/Rule

On page 303 in Peskin&Schroeder they give the vertex factor as $$V = -ie\gamma^\mu \int d^4x$$ while on page 304 they write $$V_\times = -ie\gamma^\mu\int d^4x A_\mu(x).$$ Why are the ...
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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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62 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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44 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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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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908 views

What is the commutator of an operator and its derivative?

Is it possible to calculate in a general way the commutator of an operator $O$ which depends on some variable $x$ and the derivative of this $O$ with respect to $x$? $${O}={O}(x)\\ ...
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1answer
82 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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41 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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105 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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407 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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5answers
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What exactly is $\hat{\psi}^\dagger(x)$? An operator or a function?

I've recently read Cohen-Tannoudji on quantum mechanics to try to better understand Dirac notation. A homework problem is giving me some trouble though. I'm unsure if I've learned enough yet to ...
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25 views

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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3answers
417 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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24 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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131 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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238 views

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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2answers
98 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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152 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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73 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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3answers
276 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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110 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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100 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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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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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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What is the actual significance of the amplituhedron?

The news that physicists have discovered a geometrical object that simplifies a lot our models of quantum physics has recently became viral. For an outsider like me, it is difficult to actually ...
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281 views

How to derive the form of the parity operator acting on Lorentz spinors?

I'm reading Berestetskii (Volume 4 of Landau & Lifshitz) section 19 on inversion of spinors. Berestetskii says parity $P$ maps undotted spinors into dotted spinors and vice-versa as ...