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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On weak interaction and right-handed particles

The weak interaction involving $Z^0$ boson has the following expression for its current: $$ g_{\rm{z}}J_\mu^Z = \frac{g_{\rm{w}}}{\cos \theta_W} \bar{u}\gamma_\mu \left\{g_L\frac 1 2(1-\gamma_5)+g_{R}\...
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How is the formula for specific rotation derived?

I wanted to find the complete derivation for specific rotation in chiral compounds. Where would that be available or does anyone know the derivation themselves and could share? I would want a formula ...
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Charged fermions have both chiralities, with the same mass. Shouldn’t neutrinos, also massive, have both chiralities, though with different masses?

Thanks to answers a previous question, I have realised the difference between helicity, a non-Lorentz-invariant quantity, and the Lorentz invariant chirality. Let me summarise what I understand, ...
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A thought experiment about neutrinos

I don't understand all the details of Dirac mass, Majorana mass, and many other "deep" notions. I have in mind a very simple thought experiment. Because of neutrino oscillations we know ...
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How charge conjugation operator flips chirality

I am trying to understand the charge conjugation operator by reading several references online. Until I come to a point which mention that using the anticommutation properties of the Dirac-$\gamma$ ...
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How does an axial vector field transform under a diffeomorphism?

Does it behave like a normal vector field?
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Neutrino field is left-handed

Why if we take the mass of neutrino to be zero then we get only left-handed field when $\psi_r=\frac{1}{2}(1+\gamma^5)\psi$ and $\psi_l=\frac{1}{2}(1-\gamma^5)\psi$ has no dependence on mass?
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Coefficient of effective chiral Lagrangian of $\pi\pi$ scattering

I have been suffering from the coefficient in the expansion of chiral lagrangian. Consider $$L=\frac{F^{2}}{4} \rm{Tr}(\partial_{\mu}U^{\dagger}\partial^{\mu}U),$$ where $$U=\exp(i\frac{\phi}{F}).$$ ...
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Chiral Transformation and Dirac Bilinear

I need to compute the following Dirac bilinears: $$\overline{\psi} \psi \quad \text{and} \quad \overline{\psi} \gamma_\mu \psi$$ Under the following Chiral transformation: $$\psi \rightarrow \psi' = \...
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How do massless particles have the same chirality and helicity when they are different properties?

I read this article about chirality and helicity. At some point it says For massless particles, chirality is the same as helicity. But as far as I know, helicity takes form in numbers, $(-1/2, +1/2)...
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Chiral symmetry of the Dirac Lagrangian

I need to show that in the mass to zero limit the lagrangian density: $$\mathcal{L}=\bar{\psi}(i\gamma^\mu\partial_\mu-m)\psi$$ is invariant under the transformations: $$\psi'=e^{i\alpha\gamma^5} \psi$...
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If the universe was dominated by antimatter instead of matter, would we physically notice?

I read that antimatter and matter are identical aside from their opposite charge and quantum number. Of course, the mystery of why matter dominates in our universe is an active field of research. But ...
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Two different types of circularly polarized light

Circularly polarized light [$\mathbf{E}=E_0e^{-i\omega t}(\hat{x}+i\hat{y})$] usually refers to the light whose propagation direction is perpendicular to the polarization plane, like this figure on ...
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Why does "chiral symmetry" in the Altland-Zirnbauer classification mean something different to other contexts?

The Altland-Zirnbauer classification of random matrices is based on three symmetries: time-reversal, charge conjugation, and a third which is sometimes referred to as "chiral" or "...
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Why do we use "vector-like" to mean "non-chiral", in particle physics?

I've been reading some stuff about searches for vector-like quarks and vector-like leptons, and I'm a little confused about the terminology. Also, I'm a little new to this, so bear with me. As far as ...
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Working through the solution of the Ozma problem

I’m trying to work through the Ozma problem and the Wu experiment to get a better handle on parity and I’m being tripped up by something which is almost certainly trivial. I can explain negative ...
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Transformation of Chern-Simons type action under large $SO(4)$ gauge transformation

For the Chern-Simons action $$S = \kappa \epsilon^{\mu\nu\delta}tr(A_\mu\partial_\nu A_\delta + \frac{2}{3}A_\mu A_\nu A_\delta)$$ under a large gauge transformation $$A_\mu \rightarrow g^{-1}A_\mu g +...
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Are there in nature any Right Chiral isolated electron particles?

Note: I refrain from using the concept of handedness and the terms left-handed and right-handed when referring to chirality since these usually refer to the helicity of charged fermions and their ...
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What is spectral flow of electrons?

While reading about chiral anomaly in condensed matter systems, I came across the term electron Spectral flow. I have no idea what this is and where to look for understanding this. Please help.
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The relation of gamma matrix between field operator change and chirality in Peskin and Schroeder (page 165)

I'm reading Compton scattering in Peskin's book (page 165) and there is a sentence I can't understand. The third sentence in the above paragraph says that three $\gamma$-matrix between field operator ...
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Charge term in the chiral Lagrangian with dynamical photons

When constructing the effective Lagrangian, we parametrize the Goldstone bosons (such as the pions $\pi_a$) by $U = \exp(i \pi_a \tau_a/2 f)$, where $\tau_a$ are the Pauli matrices. (See e.g. here). ...
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Chirality vs Helicity in Top Quark Decay

I still have not had a good explanation of how a Right Handed Top Quark decays. As I understand it, helicity and chirality are both a part of spin. Does this mean that if either is left handed, the ...
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Are the definitions of chirality in continuum QFT and the Nielsen-Ninomiya theorem equivalent?

I have seen two definitions of chirality in quantum field theory: According to the Wikipedia article, chirality is defined as whether a particle transforms under a left- or right-handed ...
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Are there chiral fermions in $d=4$ Euclidean space?

In $d=4$ Euclidean space the spin group is $\operatorname{Spin}(4)\cong SU(2)\times SU(2)$ where the two $SU(2)$’s are independent (as opposed to Lorentzian signature where they conjugate into each ...
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Right-handed neutrinos Lagrangian and drawing Feynman diagrams from it

The Lagrangian for the right handed neutrino field is: $$ L_{\nu} = y_{\alpha i} \bar{L_{\alpha}} H^{\dagger} N_{i} + m_{i} \bar{N^{c}_{i}N_{i}} $$ With $ L_{\alpha} $ being the left-handed lepton ...
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Where are the right-handed leptons?

So the weak force only works on left-handed leptons and quarks. Does this mean there are no right-handed leptons and quarks? If there are, why don't we see an abundance of right-handed particles that ...
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Lagrangian density transformation

In a calculation of a Lagrangian density $$ \mathcal{L}=\bar{\psi}\left(i \gamma^{\mu} \partial_{\mu}-m+i \gamma_{5} m^{\prime}\right) \psi. $$ In order to see if it is invariant or not with the ...
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Handedness over the current terms in Feynman diagrams

This is a question about the Feynman diagrams: imagine I want to calculate the following process: $$\nu_{e, L} + e^-_R \rightarrow \nu_{e, L} + e^-_R$$ I can have a t-channel diagram with $e^-_R e^-...
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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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How to show that $\bar{\psi}\gamma^{\mu}\psi$ goes to 0 if $\psi$ is are not both left/right handed?

How do you show, using the Dirac matrices, that the above expression is $0$? I have tried substituting $\psi^{\dagger}\gamma^{0}$ in for $\bar{\psi}$ but I cannot find any identities linking $\gamma^{...
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How do we show that for massless fermions, Helcity and Chirality align?

The Helicity operator of a representation of the Lorentz group is given by $$h = \varepsilon_{ijk}S^{jk}\frac{P^i}{|P|}$$ where $S^{\mu\nu}$ are the generators of the Lorentz group. In the $(\frac{1}{...
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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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How to calculate the branching fraction of hadrons? Or good resources on chiral perturbation theory

I am wondering how I could calculate branching ratios (or any effective diagram) for various hadrons. In particular I am interested in a rare pion decay via a virtual photon:$\pi^0\to \gamma \gamma^* \...
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Why three gamma matrix between initial and final electron lead to the same helicity?

Quote Peskin page 165 Suppose that the initial electron is right-handed... Since this term contains three $\gamma$-matrix in (5.97) between $\bar u$ and $u$ the final electron must also be right-...
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Chirality/helicity of anti-particles (again)

Questions (very) closely related to this one have been posted dozens of times, but the joint information (including even lecture notes and books) is incredibly contradictory, so I state my specific ...
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Anticommutation relation for the Weyl spinors in Minkowski space+time

For $D$-dimensional Minkowski space+time, I suppose that the Dirac spinor has the following anticommutation relation: $$ \{ \psi(x_1), \psi(x_2)\}=\{ \psi^\dagger(x_1), \psi^\dagger(x_2)\}=0 $$ $$ \{ \...
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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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Is an Anti-positron actually only a relativistic effect on the observed helicity of an electron?

I have read quite recently this article here: https://www.quantumdiaries.org/2011/06/19/helicity-chirality-mass-and-the-higgs/ in which it is explained that an Anti-positron is actually a different ...
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