# Questions tagged [chirality]

Chirality is defined through the ±1 eigenvalue under action of γ^5 on ψ, a Dirac field thus projected into its left- or right-handed component by the projection operators (1−γ^5)/2 or (1+γ^5)/2 on ψ. For massless particles (only!) chirality coincides with [helicity], a notion which is frame-dependent, and hence ambiguous for massive particles. Avoid using the [helicity] tag instead: the projectors *must* be implied.

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### When we talk about the helicity of a particle, why are we (apparently) ruling out the cases of the spin being perpendicular to the motion direction?

If I assume the (linear) momentum is in the direction of the X-axis, could I NOT find the spin-up in the positive Y-(or Z-) axis and the spin-down in the negative Y-(or Z-) axis?
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### Spontaneously Broken Approximate Symmetry, Weinberg 19.4, QFT 2

I am having difficult time understanding part of 19.4 section where Weinberg introduces the symmetry breaking terms for $SU(2)\times SU(2)$ symmetric theory for $u,d$ quarks, specifically, he adds (eq....
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### Prove that Majorana mass term is Lorentz invariance

I have a homework to prove that using one kind of chirality, let's say left-handed, we can construct a mass term. The argument is to show that this term $\psi^TCP_L\psi$ is satisfy the dimensionality ...
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### Fermi's theory and left-handed anti-neutrino

I calculated the $\mu \rightarrow e^- + \nu_{\mu} + \bar{\nu}_{e}$ both in Fermi's theory (V-A) and Intermediate Vector Boson theory and IVB at first order seems to match with Fermi's theory which is ...
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### What are the real Electromagnetic fields of Circularly Polarized Light?

It is my understanding that the $\vec{E}$ and $\vec{B}$ fields of a circularly polarized photon sit purely in the $(1,0)$ or $(0,1)$ representation of the (complexified) Lorentz Group, and have ...
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### How to convert a singlet current in electroweak theory to a doublet current?

I am referring to an aspect of Glashow-Salam-Weinberg theory of leptons. More specifically a step in the book 'Gauge Theory of Weak Interactions' by Walter Greiner page 147. We can write the ...
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### Difference between right-handed and sterile neutrinos

Several SM extensions propose the addition of heavy, right-handed neutrinos to explain the smallness of neutrino masses. There are also theories adding a fourth, sterile neutrino in the context of ...
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### Twisted Bilayer graphene effective model (Model for the metal-insulator transition in graphene superlattices and beyond)

This question is referred to the article "Model for the metal-insulator transition in graphene superlattices and beyond" The hamiltonian H1 is written using chiral basis. Can someone direct ...
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### Chiral anomaly of Weyl fermion is half of Dirac

How can one mathematically see that the anomaly for a Weyl fermion is half of Dirac in the Fujikawa path integral method? Edit I do understand that a Dirac fermion is two Weyl fermions. What I wish to ...
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### Parity and chirality [closed]

I don't exactly understand how parity is related to chirality. On wikipedia it says that the parity transformation can be thought of as a test for chirality of a physical phenomenon. How those two ...
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### Why do we care about chirality?

I'm trying to figure out what's the importance of chirality in QFT. To me it seems just something mathematical (the eigenvalue of the $\gamma^{5}$ operator ) without any physical insight in it. So my ...
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### Chirality effect in graphene [duplicate]

My BS research topic is 2-D nanomaterials. Currently, I am researching different 2-D nanosheets including graphene, silicene, and other elements of group IV-A. I study the chirality effect in them. I ...
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### Are chiral fermions and chiral bosons equivalent in a chiral Lagrangian?

Is it equivalent to talk about a chiral theory in terms of 1. chiral fermions which are differently coupled to the gauge field or 2. fermions coupled to a "vector minus axial" gauge boson? ...
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### What's the origin of the chirality selection rule?

I'm reading this paper on Circular Photogalvanic Effect (https://www.nature.com/articles/nphys4146) and they mention a "chiral selection rule": Chirality selection rule: Right-handed ...
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### Confusion regarding PCAC for negative pion

I'm really confused about how the PCAC condition should be written for the negative pion, and also confused about the two different conventions for the pion decay constant which are related by a ...
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