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 can we approximate dynamics of massive particles by masless and vice versa?

I am puzzled by the following observation. Our descriptions of massless and massive particles are very different. For example, masless particles have only two polarizations, which we call helicities. ...
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2answers
83 views

What is the program of quantum field theory? What is its derivation?

Paraphrasing Griffith's: For some particle of mass m constrained to the x-axis subject to some force $F(x,t)=-∂V/∂x$, the program of classical mechanics is to determine the particle's position at any ...
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45 views

Thermal mass and Thermal Width

I have a question about understanding the physical interpretation of the thermal mass and width of a particle. If we consider a particle in a plasma (which lets say is in the early universe and so ...
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Complex integration by shifting the contour

In section 12.11 of Jackson's Classical Electrodynamics, he evaluates an integral involved in the Green function solution to the 4-potential wave equation. Here it is: $$\int_{-\infty}^\infty dk_0 \...
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47 views

Spontaneous symmetry breaking of gauge symmetry in 1+1 dimensions?

The Mermin-Wagner theorem states that continuous global symmetries cannot be broken in two or fewer spacetime dimensions; however, I have not seen this statement applied to gauge theories. Does it ...
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1answer
213 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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377 views

What's the Coulomb Branch and why is it important?

I'm studying the introduction of flavour degrees of freedom in the AdS/CFT correspondence and now I'm supposed to calculate the mass spectrum of mesons in the Coulomb branch. I have searched the ...
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1answer
89 views

Why is it correct to estimate divergences by the cutoff in QFT?

Let's say we have a linear divergence in a quantum field theory. The way to deal with this infinite quantum correction is to go through the whole process of renormalization. However, quite often, ...
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2answers
58 views

Why is the infinitesimal SUSY variation generated by the sum of a left- and right-chiral generator

I was wondering why in many (all? e.g.https://arxiv.org/abs/hep-ph/9709356) resources on N=1 SUSY the variation of a field in the simplest free susy model is defined as $$\delta_\epsilon \phi = (\...
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Srednicki's QFT: Feynman Rules and Feynman Diagrams

I'm reading Srednicki's Quantum Field Theory. I 'm trying to read Srednicki's presentation of Feynman Diagrams in the chapter Path Integral for the Interacting Field Theory. The path integral for the ...
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1answer
771 views

What is “localisation” of instantons?

I often encountered the term "localization" in the context of instantons, as for example in the work of Nekrasov on extensions of Seiberg-Witten theory to ${\cal N}=1$ gauge theories. Could someone ...
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140 views

What happens to Goldstone bosons in the Higgs potential after symmetry breaking?

When the gauge symmetry of our Lagrangian breaks spontaneously through the Higgs mechanism, we usually find that $n$ Higgs degrees of freedom become massless through the vacuum expecation value (vev), ...
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Translational symmetry and generalized Heisenberg equation of motion [on hold]

Suppose, there are 2 plates; one at x=0 and another at x=L such that the area vector of the plate surface is parallel to the x axis and electromagnetic field is confined between this plates. I am ...
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24 views

Feynman Rules and Feynman Diagrams in QFT by Srednicki [duplicate]

I'm reading Srednicki's Quantum Field Theory. I 'm trying to read Srednicki's presentation of Feynman Diagrams in the chapter Path Integral for the Interacting Field Theory. Link to the textbook: http:...
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1answer
46 views

Interpretation of the vector current in field theory

In field theory we write $$J^\mu=\bar{\Psi}\gamma^\mu\Psi$$ But I can't understand why it is so. Could anyone explain each of the terms in the multiplication?
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1answer
48 views

How to understand CP-violation in kaon systems with Feynman diagrams and matrix elements?

I am trying to understand CP-Violation in the Kaon system using feynman diagrams and matrix element. Here is a slide from Mark Thomson corresponding exactly to what I am looking for (http://www.hep....
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1answer
52 views

Gauge Theory of Superconductors

I'm trying to understand better the nature of the gauge redundancy and the Higgs mechanism in superconductors. Specifically, I'm looking for a good reference that explains monopoles, vortices, and ...
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3answers
293 views

Dummy variables in Dyson series

In the Dyson series, it is known that: \begin{align} {\cal T}\exp\left[-\frac{i}{\hbar}\int_0^tH(t')dt'\right] &= I - \frac{i}{\hbar} \int_{0}^{t} dt' H(t') + \left(-\frac{i}{\hbar}\right)^2 \...
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1answer
73 views

Problem with figuring out sign conventions in QFT

I have a problem with sign conventions in QFT which I have trouble dealing with myself. I self-study and mainly use Weinberg and Peskin. I will present the reasoning following conventions adapted by ...
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1answer
240 views

Has Sen quantized superstring fields?

Today I saw a paper by Ashoke Sen titled "BV Master Action for Heterotic and Type II String Field Theories". Is it really the "quantization" of superstring fields for the first time? What can be its ...
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1answer
64 views

Integral form of solution of Dyson series and differentiation of the exponential form

The solution to time dependent hamiltonian equation is: $$\frac{\partial}{\partial t}U(t) = -\frac{i}{\hbar}H(t)U(t)$$ The immediate integral form solution is $U(t) = I - \frac{i}{\hbar}\int_{0}^{...
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39 views

A question about the Ward-Takahashi identity

I am studying Peskin and Schroeder's textbook of quantum field theory. I have proceeded to Ward-Takahashi identity and have one question. Eq.(7.66) and Eq.(7.67) are the two cases involved. Then ...
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1answer
129 views

Commutation relations in second quantization

I know that for operators $a(\chi_1), a(\chi_2)$ of the same type (fermionic or bosonic) $$ [a(\chi_1), a(\chi_2)]_{-\xi} = [a^\dagger (\chi_1), a^\dagger (\chi_2)]_{-\xi} = 0 \tag{1}$$ where $$\xi ...
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1answer
184 views

Why do we need to build photon colliders? Since electron-position colliders are very “clean”

What's the advantage of gamma-gamma colliders? What new physics can be done with it? Reference: http://www.slac.stanford.edu/pubs/beamline/26/1/26-1-kim.pdf
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140 views
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Why is this expression infrared divergent

On P.217 of Quantum Field Theory by Peskin and Schroeder, it is stated that the Eq.(7.16) is infrared divergent and therefore a small photon mass $\mu$ is added to the photon propagator. The equation ...
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350 views

Why can't a real scalar couple to the electromagnetic field?

If we have a complex scalar $\phi$ we know that the gauge-invariant interaction with $A$ is given by $A^\mu J_\mu$, where $J$ is the Noether current of the $U(1)$ symmetry of the Lagrangian $$ J_\mu\...
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1answer
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three-particle quantum entanglement

So I know that two particles can be entangled in a quantum way, but is it possible that more than two particles be entangled in a quantum way? Most descriptions provide with two-particles cases, so I ...
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0answers
32 views

What is the recursive relation for three-particle Green's functions?

In condensed matter physics, one often choose to study the many-body Green's functions (GF) with the diagram (perturbation) expansion technique. In what follows only two-body interaction is concerned. ...
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1answer
375 views

Relation among anomaly, unitarity bound and renormalizability

There is something I'm not sure about that has come up in a comment to other question: Why do we not have spin greater than 2? It's a good question--- the violation of renormalizability is linked ...
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2answers
329 views

Lepton masses in the Standard Model

Some simple questions regarding leptonic masses in the Standard Model (SM): Why there is not an explicit mass term in addition to the effective mass term that arises from the Yukawa terms after ...
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3answers
361 views

Do all the particles acquire mass in the Standard Model due to the Higgs mechanism only?

I know that a mass term for an intermediate boson is not compatible with the gauge symmetry. But in principle a mass term for the electron field does not violate a gauge symmetry. However to build an ...
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1answer
129 views

Normal Ordering in String Theory: Polchinsky vs. all others

Polchinsky defines normal ordering in string theory as: $$:X^\mu(z,\bar z)X^\nu(w,\bar w): = X^\mu(z,\bar z) X^\nu(w, \bar w) + \frac{\alpha'}{2} \eta^{\mu\nu} \log |z-w|^2$$ and for more ...
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161 views

Completeness Relations of Polarization Vectors in QCD

What are the completeness relations of the polarization vectors of (external) particles in QCD amplitude calculation? (I assume the polarization vectors depend on the gauge and even so still have some ...
3
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1answer
123 views

What is the axial current?

The axial current is defined as $$j^\mu_5 = \bar{\psi} \gamma^\mu \gamma_5 \psi.$$ This quantity is important when studying anomalies. Explicitly working out components, the axial current is just the ...
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47 views

Time ordered product of operator and Heisenberg equation of motion [on hold]

Can we use time ordered product of operators in Heisenberg equation of motion? Please give me an example.
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1answer
326 views

In QFT, why do fermions have to anticommute in order to insure causality?

I have seen this question and I believe I understand the answer to it. However, AFAIK, only for bosons the causality condition is a vanishing commutator. For fermions we expect the anticommutator $[\...
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3answers
40 views

Notation about basis of gamma matrices in $4d$

In Quantum Field theories, we encounter gamma matrices a lot. Reading from various textbook, i encountered some textbook use different basis for their gamma matrices. Gamma matrices are defined such ...
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36 views

Fermi's golden rule and S-matrix

As I understand, Fermi's golden rule is a result from first order perturbation, which says that the transition rate of an initial state $|i\rangle$ to a final state $|f\rangle$ is $$ \Gamma_{i\...
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1answer
1k views

Is the Lagrangian density in field theory real?

As the Lagrangian in classical mechanics corresponds to energy, it must be real. But is that the case in quantum field theory? I mean, it should still correspond to some sort of energy, but what about ...
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42 views

Hermiticity of the Lagrangian density [duplicate]

In quantum mechanics, the dynamical variables are replaced by hermitian operators. However, the Lagrangian density in quantum field theory is not an observable but we also make sure that it is ...
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1answer
52 views

The relation between critical surface and the (renormalization) fixed point

In the book, I read some remarks about the criticality: Iterations of the renormalization (group) map generate a sequence of points in the space of couplings, which we call a renormalization ...
6
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2answers
323 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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0answers
55 views

Renormalization group equation: physical meaning of energy scale [duplicate]

I'd like to understand the physical meaning of the energy scale $\mu$ that emerges in the renormalization group equation (RGE). In particular I don't understand in what way a running coupling constant ...
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0answers
192 views

Interpreting the Klein-Gordon Annihilation Operator Expression

I can derive $$a(k) = \int d^3 x e^{ik_{\mu} x^{\mu}} (\omega_{\vec{k}} \psi + i \pi)$$ for a free real scalar Klein-Gordon field in three ways mathematically: the usual Fourier transform way in ...
3
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1answer
604 views

Gradient involved commutator in $\phi^4$ theory

In a phi fourth theory, the Hamiltonian density is: $$\mathcal{H}=\frac{1}{2}\pi^2+\frac{1}{2}(\nabla \phi)^2+\frac{1}{2}m^2\phi^2+\frac{\lambda}{4!}\phi^4$$ Now I impose the usual equal time ...
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1answer
41 views

Distributive property of the time-ordering symbol

Most derivations of the LSZ reduction formula, e.g. Srednicki (equations 5.13, 5.14, 5.15), Schwartz (equations 6.17, 6.18, 6.19), Wikipedia use a property of the time-ordering symbol that looks like ...
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1answer
630 views

How do instantons cause vacuum decay?

From what I read about on instantons (Zee, QFT in a Nutshell, pg 309-310), an instanton is a vacuum solution that maps $S^3 \rightarrow S^3$ (the boundary of Euclideanized spacetime), which comes from ...
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1answer
59 views

Srednicki's Path Integrals: Ground-State to Ground-State Transition Amplitude in the Presence of a Perturbation

Srednicki's Quantum Field Theory mentions the following at the end of the unit on path integrals in non-relativistic quantum mechanics: Assume that the total Hamiltonian is of the form, $$ H = ...
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21 views

Local Effective actions

While studying partition functions in general, i came across a statement which says that "the partition function of a theory without gapless excitations must be a local functional of the background ...
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1answer
64 views

Does Microcausality follow from Lorentz Invariance?

In a Lorentz Invariant theory, does microcausality automatically hold? In a free theory this is obvious. In an interacting theory I found some 'proof's in this paper: http://arxiv.org/abs/0709.1483 ...