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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296 views

Does the concept of both helicity and chirality make sense for a massive Dirac spinor?

Does the concept of both helicity and chirality make sense for a massive Dirac spinor? A massive electron in the chiral basis is written as a column made up of $\psi_L$ and $\psi_R$. What is the ...
3
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1answer
472 views

Width of a photon. And its length

Everyone is always talking about photon's wavelength. But what about its dimensions? What is length and width of it? And does it even have a point to think about such things? Or those dimensions are ...
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vote
1answer
102 views

Invariance under charge conjugation… Or not?

I have read some paper which says that the electroweak Lagrangian includes these terms like $\bar{\psi} \gamma_a\gamma_5\psi$ and $\bar{\psi} \gamma_a \psi$. They violate charge conjugation symmetry. ...
8
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1answer
131 views

Why do we require quantum fields to vanish at infinity?

Classical fields, like the electrical field must vanish at infinity, because otherwise their energy would be infinite. This can be used in computations to exclude certain solutions. In quantum ...
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1answer
99 views

Renormalization condition

Can any on explain to me, why renormalization condition $$\Sigma(\gamma_\mu p^\mu=m)=0,$$ for one loop implies $$\Sigma_2(m)=m\delta_2-\delta_m~?$$ In the original $\Sigma_2$ we had $ m_0$ which is ...
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1answer
288 views

How do I solve this Gaussian path integral?

Suppose $$ Z = \int \mathcal D[\phi^*] \mathcal D[\phi] \exp(\phi^*A\phi + \phi B\phi) $$ where $A$ and $B$ are operators. I know how to solve a Gaussian path integral involving only $\phi^* A \phi$ ...
3
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1answer
46 views

In what sense is the chiral decomposition of spinors unique?

We may decompose a spinor field $\psi = \psi_L + \psi_R$ where $\psi_L = \frac12 (1 - \gamma^5) \psi$ and $\psi_R = \frac12 (1 + \gamma^5) \psi$. (I believe this is because the clifford algebra has ...
7
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1answer
151 views

What is the quantum state of a static electric field?

This is something that I've been curious about for some time. A coherent, monochromatic electromagnetic wave is well described by a coherent state $|\alpha\rangle$. The quantum treatment of the ...
3
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0answers
64 views

Matter antimatter fundamental and adjoint representation (Hermitian Anti-Hermitian)

I’m struggling with the following. I read in “The Standard Model: A Primer by Cliff Burgess”, page 493, that fermion fields in the fundamental representation can be thought of as column vector(s) ...
0
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1answer
21 views

Chrial multiplet's fundamental and anti-fundamental representation

Here i follow the notation in arXiv 9312104v1 (Witten's Verlinder algebra ~ paper) The usual kinetic energy for a chiral multiplet is given as (In 2 dimensional $N=(2,2)$ supersymmetry theory) ...
1
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1answer
44 views

Trace of derivatives of unitary operators [closed]

I have been studying some lecture notes on the non-linear sigma model and I came up with some difficulties involving a trace. I have the following unitary operator $$ U=\exp\left( ...
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0answers
66 views

Field renormalization of scalar Yang-Mills

In most books, one can find the field renormalization $Z_3$ in Yang-Mills with fermionic matter in the fundamental. In the $\overline{MS}$ scheme, tt is given by $$ Z_3 = 1 + \frac{g^2}{16\pi^2 ...
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0answers
50 views

How to deal with coupled fermion boson operators?

I am a beginner in field theory and I have an exercise where I have a product of coupled fermion boson operators? $$ \hat{b_{l} }^{\dagger}\hat{c_{l^{'}} }^{\dagger}\hat{a_{q} }\hat{b_{l} ...
4
votes
1answer
90 views

Number of Goldstone bosons in paramagnetic-to-ferromagnetic phase transitions

In paramagnetic-to-ferromagnetic phase transitions, the symmetry spontaneously breaks down from SO(3) to the subgroup SO(2) below $T_\text{crit}$. This implies that there should be two Goldstone modes ...
9
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1answer
144 views

What exactly do we mean by symmetry in physics?

I'm referring here to invariance of the Lagrangian under Lorentz transformations. There are two possibilities: Physics does not depend on the way we describe it (passive symmetry). We can choose ...
3
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1answer
78 views

One loop tadpole diagram $\phi \to \phi$ in $g\phi^3$ theory

I am trying to evaluate the tadpole diagram of $\phi^3$ theory to practice one loop amplitudes, but I am stuck at a certain point. The amplitude is given by the integral, $$\mathcal{M} = ...
3
votes
2answers
126 views

Global symmetry and particle multiplets

In chapter 20, of Peskin and Schroeder's quantum field theory book, they start with a comment that a global symmetry that is manifest lead to particle multiplets with restricted interactions. Can ...
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0answers
21 views

Why third Pauli $\tau_3$ becomes third Isospin component $\tau_3^{<\Phi>}$?

When considering the higgs coupling to the neutral gauge boson of EW theory (see e.g. C. G. Tully (EPP nutshell) page 102): $$\tag{1}\mathcal{L} = \frac{1}{4}\left\{\left(g' B_\mu Y_\Phi+gW_\mu^3 ...
1
vote
1answer
210 views

How does QFT interpret the Negative probability problem of the real scalar fields' Klein-Gordon equation?

I am totally a beginner in QFT, here's the problem that I got: for the real scalar fields, are there any elementary particles descriped by them. If so, how to understand the negative probability ...
2
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0answers
38 views

Why scattering of red and blue quark only involves $G_8^\mu$?

According to the author C. G. Tully (Particle physics in a nutshell), the scattering of a red and blue quark only involves $G_8^\mu$. How come this is so? I thought $G_3^\mu$ and $G_8$ only mediate ...
2
votes
1answer
67 views

What would be the most general effective Lagrangian involving one Higgs and two gluons?

Two different possibilities come into my mind $\mathcal{L}\sim{}HG_{\mu}G^{\mu}$ where $G^{\mu}$ is the gluon field and $H$ the Higgs, or either $\mathcal{L}\sim{}HG_{\mu\nu}G^{\mu\nu}$ Where ...
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1answer
47 views

Evaluation Feynman parameters from denominator

I try to evaluate Feynman parameters but got stuck at some point. $$ \int_0^1 \frac{1}{(Ax+(1-x)B)^2}\,dx=\frac{-1}{(Ax+B(1-x))}\frac{1}{A-B}=\frac{1}{AB} $$ $$ \frac{1}{AB}=\int_0^1 \int_0^1 ...
2
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0answers
44 views

't Hooft many instanton solutions

I'm study 't Hooft many instanton solutions of self-duality equation. In this method $A^a_\mu=-\bar{\eta}^{a}_{\mu\nu}\partial^\nu \ln{\Phi}$. After substitution in self-duality equation I've proven ...
7
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2answers
672 views

Does anyone take the Wightman axioms seriously?

Does anyone take the Wightman axioms seriously? Mainly with respect to quantum gravity or gauge theores, abelian or non-abelian? Anyone doing any research on axiomatization of QFTs in some way?
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0answers
91 views

Klein-Gordon field commutator integral identity [closed]

Consider a Klein-Gordon field $\phi$ on points $x,y$ of $\mathbb R^4$ Minkowski-spacetime. Here I'm writing $x=(x^0, \stackrel \rightarrow x)$ so that $\stackrel \rightarrow x$ gives the spatial ...
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3answers
100 views

Klein Gordon for spin-1 particle photon

If Klein Gordon equation is for spin-0 particles, I write massless fields as $\square A=0$, how can I say $A_\mu=\epsilon^\mu e^{-ikx}$ as a wave function of polarized photon (spin-1) ?
13
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1answer
1k views

Difference between 1PI effective action and Wilsonian effective action?

What is the simplest ay to describe the difference between these two concepts, that often go by the same name?
4
votes
1answer
61 views

Variation of the kinetic quark term of the QCD Lagrangian under gauge transformation

A simple kinetic quark term would look like $$\bar{\psi}(\gamma^{\mu}\partial_{\mu} - m){\psi}.$$ Imposing SU(3) symmetry the Dirac spinor transforms like $$\psi(x) \rightarrow \psi'(x) = e^{ig_s ...
1
vote
1answer
63 views

difference between classical vacuum solutions and instantons

What does the classical vacuum of the $SU(2)$ Yang-Mills action correspond to? Does it correspond to $F_{\mu\nu}=0$ everywhere or just at the spatial infinity? In Srednicki’s book, he has shown that, ...
2
votes
2answers
208 views

Derivation of (2.45) in Peskin and Schroeder

I'm having trouble understanding the step $$\left[\pi (\vec{x},t),\int d^{3}y ~(\frac{1}{2} \pi (\vec{y},t)^{2}+\frac{1}{2}\phi (\vec{y},t)(-\nabla^{2} +m^{2})\phi (\vec{y},t)) \right]$$ $$ =\int ...
8
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3answers
2k views

Noether theorem, gauge symmetry and conservation of charge

I'm trying to understand Noether's theorem, and it's application to gauge symmetry. Below what I've done so far. First, the global gauge symmetry. I'm starting with the Lagragian ...
1
vote
2answers
63 views

SU(2) kinetic term as a trace

Is there a easy way to rewrite the SU(2) kinetic term as a trace? As in $$\mathcal{L} = -\frac{1}{4}\vec{F}_{\mu\nu}\vec{F}^{\mu\nu}\\[1cm] = -\frac{1}{2}\mathrm{tr}\Bigg[\bigg(\vec{F}_{\mu\nu}\cdot ...
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0answers
28 views

A question about the interchanges of particles belonging to species in Weinberg's QFT book 1

Weinberg put this in page 171 that I can't quite understand: If we like, we can avoid this question by simply agreeing from the beginning to label the state-vector by listing all photon momenta and ...
5
votes
1answer
117 views

Is there a way to get the spin naturally in nonrelativistic theories?

We all know how spin is added in a rather ad-hoc way in quantum mechanics. In the other hand, in relativistic quantum field theories the spin structure arises quite naturally from the fields. Is ...
2
votes
2answers
88 views

Group representation acting on operators (QFT)

I have found in many texts the following statement: Let $T_g$ be a representation of a group (of transformations, e.g. rotations, translations, Lorentz transformations ) acting on a given Hilbert ...
2
votes
2answers
58 views

Showing that a bilinear variation is Lorentz invariant

Let $\psi, \chi$ be a spinor (say Dirac). Then the infinitesimal Lorentz variation is given by $$\delta \psi = -\frac{1}{4}\lambda^{\mu \nu} \gamma_{\mu \nu}\psi$$ then I think that the conjugate is ...
4
votes
1answer
31 views

Going from width to cross section

Given the decay width of a process, $\Gamma(A\to B+C)$, is it possible to turn this around to find the production cross section, $\sigma(B+C\to A)$? Edit: In particular I have been thinking of ...
8
votes
1answer
154 views

Do we need new physics to supercede triviality?

I've been reading about the higgs triviality bound (see for example here). It is discussed that the higgs self coupling at some energy scale becomes non-perturbative. If the higg's mass is above about ...
2
votes
0answers
56 views

Physical significance of Dirac equation in (2+1)-D

What's is the physical significance of the two inequivalently irreducible-represented Dirac equations in (2+1)-D? As it is known, all the $4\times 4$ matrix representations of the Dirac algebra ...
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0answers
36 views

Variational calculus needed for QFT [duplicate]

Where can one learn the variational calculus needed for QFT? Im not sure a whole book of super rigorous treatment is what i need.
1
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1answer
60 views

Baryogenesis via Leptogenesis

Baryon number is directly violated through electroweak anomaly and so does the Lepton number, for each transition from one vacuum to another. The two violations are of equal amount $\Delta B=\Delta ...
3
votes
2answers
354 views

What's the boundary of microscopic world and macroscopic world?

In other words, what's the maximum size of a Quantum denizen upto which it shows Quantum behaviors? How big do I need to create a molecule (or, collection of molecules) so that Feynman's multiple path ...
4
votes
1answer
116 views

In QFT, do the fields evolve with determinism, in principle?

In quantum mechanics, the outcomes of a certain measurement might not be deterministic. However, the wavefunction evolves with determinism according to Schrodinger's equation. Is QFT analogous in ...
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2answers
201 views

Why would electrons have Weak Charge? [closed]

Electrons (and, their cousins Muon and Tau) carry Weak Charge having value $-1/2$. If you believe in Strong Anthrophic Principle Why does electrons carry Weak Charge? If you don't believe in Strong ...
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0answers
44 views

Colour decomposition in QCD

I am looking to compute the matrix element for the process gg -> u ubar at leading order. It is straightforward to calculate the non-colour part of the usual s, t and u channels. I will call these ...
2
votes
1answer
59 views

Quick non rogorous way to obtain Feynman rules from a Lagrangian in a non abelian theory

I have been told that a quick way to get the Feynman rules from a Lagrangian is to take an interaction term, forget about the fields and multiply an $i$. This works perfectly for example for QED but I ...
3
votes
1answer
149 views

Why is there sometimes an additional term in the orthogonality relations for the polarization vectors?

When considering the polarization vectors of a massive spin-1 field, like an $A_\mu$ with Lagrangian density $$ \tag{A} \mathscr{L} = - \frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{1}{2}M^2 A_\mu A^\mu,$$ ...
0
votes
1answer
48 views

Relation between $a_{-p}$ and $a^{\dagger}$? for real scalar field

Fast question. Consider the real Klein-Gordon field. Is there a way to relate $a_{-p}$ with $a_p^{\dagger}$?
2
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0answers
74 views

Stack presentations and massive non-conformal theories

In the paper, Cluster Decomposition, T-duality, and Gerby CFT’s , by Hellerman, Henriques, Pantev and Sharpe, in the introduction it says: "Briefly, the idea is that nearly every stack has a ...
4
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1answer
107 views

Renormalization in Classical Field Theory

1) The statement that general relativity (GR) is not renormalizable - is it a statement only about the quantization of GR or is it non-renormalizable also as a classical field theory? 2) More ...