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2
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2answers
32 views

Fierz Reordering of Gamma Matrices and Spinors

I was looking for Fierz rearrangement for Gamma matrices in the context of Chiral Fermions but couldn't find a simple introductory level lecture note/book ! Here's what I want: I have this ...
1
vote
0answers
30 views

Antiparticles, charge conjugation and chirality

(Why/how) are antiparticles and charge-conjugates different things? I am trying to understand the effect of discrete symmetries on spinor fields (neutrinos in particular). In the article, Dirac, ...
5
votes
1answer
46 views

The chirality of (2+1)D Dirac equation

Are there any definitions about the chirality of (2+1)D Dirac equation? For the (3+1)D Dirac equation, the Dirac field can be written as the sum of left- and right-hand Weyl field. Can this be reduced ...
1
vote
0answers
37 views

Does charge conjugation affect parity?

Notice that these transformations do not alter the chirality of particles. A left-handed neutrino would be taken by charge conjugation into a left-handed antineutrino, which does not interact in ...
1
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0answers
40 views

Mass and wave function renormalization In chiral perturbation theory

Before I put forward my actual question, I think it will be useful to set the context in a clear way and that involves my understanding of a few very basic things of Chiral Perturbation Theory. ...
4
votes
1answer
97 views

Why is the chiral symmetry only $SU(3) \times SU(3)$ and not $SU(6)$?

In the limit where the masses vanish, low energy QCD has a well known chiral symmetry (see http://arxiv.org/abs/hep-ph/0505265 for a very extensive review, and pg 19 for the section relevant for my ...
0
votes
3answers
106 views

Why isn't $\bar \psi_L \psi_R$ zero?

My book gives this Lagrangian: $$ L = -|\partial \phi|^2 -V(\phi) -\bar \psi_L \not \partial \psi_L -\bar \psi_R \not \partial \psi_R -g(\phi \bar \psi_L \psi_R + \phi^* \bar \psi_R \psi_L) $$ It's ...
5
votes
2answers
87 views

SU(3) singlets and triplets

I was reading my prof's notes and came across a passage that I didn't understand: Consider a chiral SU(3) symmetry, under which the left-handed parts of the spin-1/2 fields of a fermion-number- ...
2
votes
1answer
42 views

Parameterization of an arbitrary element of $U(2)_L \times U(2)_R$ (Chiral symmetry with two quarks)

When you write down the Lagrangian for two quarks : \begin{equation} \mathcal{L}_\text{QCD}^0 = -\frac{1}{4} G_{\mu\nu}^a G^{a\mu\nu}+ \bar\Psi i \gamma^\mu D_\mu \Psi \end{equation} you find an ...
1
vote
1answer
188 views

Why are right hand neutrinos unaffected by all forces except gravity

I'm curious as to something I read on Berkeley's website. Does anyone happen to know why, according to this model,right hand neutrinos are unaffected by all forces except gravity? (Model taken from ...
0
votes
1answer
81 views

Why would it transform like this under chiral symmetry?

Why would a $2 \times 2$ matrix of spinless fields $\Sigma$ transform as follows under the chiral symmetries? $$\delta \Sigma = i \epsilon_{L} T_a \Sigma - i\Sigma \epsilon_RT_a$$ Primary written on ...
1
vote
0answers
31 views

Energy levels for nonlinear Dirac equation

Let's have equation $$ \left( i\gamma^{\mu}\partial_{\mu} - m + a\bar{\psi}\gamma_{5}\gamma_{\mu}\psi \gamma_{5}\gamma^{\mu}\right)\psi = 0. $$ Here $a$ is constant. I need to evaluate energy levels ...
1
vote
0answers
41 views

Fujikawa method for arbitrary transformations

When the Fujikawa method is presented in every book I've read so far, the transformation is initially written as $e^{i\chi (x) \gamma^{5}}$. The trace of $i\chi(x)\gamma^{5}$ is done by including a ...
4
votes
1answer
107 views

How can we measure chirality in experiments?

Chirality is a concept quite different from helicity. These two concepts only happen to have the same numerical value for massless particles. I understand that we can measure helicity, but how can we ...
3
votes
1answer
94 views

Pion decay: V-A vs. V coupling

For the Decay $$ \pi^+ \to \mu^- \bar{\nu}_\mu $$ the Feynman rules for this tell us that the vertex couples with $\gamma^\mu (1-\gamma^5) / \sqrt{2} $. This gives me the reduced amplitude of $$ M = ...
1
vote
0answers
15 views

Explain materials with 4 fold symmetry having same reflectance when shone with LCP and RCP

This is my first post here. I am currently reading "Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation" by Do-Hoon Kwon, Pingjuan L. Werner, and ...
5
votes
5answers
328 views

Is Parity really violated? (Even though neutrinos are massive)

The weak force couples only to left-chiral fields, which is expressed mathematically by a chiral projection operator $P_L = \frac{1-\gamma_5}{2}$ in the corresponding coupling terms in the Lagrangian. ...
5
votes
0answers
94 views

If weak isospin is not conserved in time, what does the Noether theorem tell us?

As far as I understand weak isospin is only conserved in interactions but not as time evolves. Nevertheless, we get from Noethers theorem, because of global $SU(2)$ invariance a conserved quantity ...
4
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2answers
473 views

Why photon only have helicity other than spin? [duplicate]

When learning angular momentum in quantum mechanics, a spin 1 particle have 3 states. Then I saw from sakurai's modern quantum mechanics that photon's two polarization are just like spins, but with ...
10
votes
3answers
420 views

Are there really left-chiral particles?

A chiral eigenstate is always a linear combination of a particle and an antiparticle state and a particle or antiparticle state is always a linear combination of chiral eigenstates. Now, how can we ...
5
votes
1answer
133 views

Are the left-chiral and right-chiral yukawa couplings equal?

I guess another way to ask this is: Does the "physical electron" spend EQUAL time being a left-chiral and right-chiral fermion, on average? Clarification: The electron switches between (-1/2 T3, -1Y) ...
0
votes
1answer
303 views

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 ...
1
vote
0answers
37 views

What is a Chiral Algebra for a group?

What do we mean by the Chiral Algebra for a group G (SO(3) etc )? Do you know a reference suitable for physicists? Thank you
3
votes
0answers
202 views

Charge conjugation and chirality

while I was reading about charge conjugation I found some (apparently) contradictory facts. For example Itzykson & Zuber says (page 153) "Up to a phase, $\cal C$ interchanges particles and ...
6
votes
1answer
453 views

Chiral anomalies

Recently I have read that there is contraction of chiral anomalies in SM. But people are working on chiral anomalies theory. So I have the question: what is the importance of development of the theory ...
2
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0answers
148 views

Anomalies in QFT books

Why in most QFT books when author discusses of non-invariance of measure of path integral (massless fermions interact with gauge fields) $$ \int D\bar{\Psi} D\Psi \to |\Psi \to U\Psi , \quad ...
3
votes
0answers
69 views

States of “positronium” with chiral fermions?

When I combine positron and electron to form positronium, or generically two spin 1/2 particles, I have four possible spin combinations that arrange into a singlet and a triplet state, which in turn ...
5
votes
0answers
100 views

Can you gauge a $U(1)_L$ symmetry?

I recently calculating the one loop correction for the propagator of a gauge boson, $\hspace{5cm}$ I assumed arbitrary left and right couplings, $ g _L $ and $ g _R $. I found that the one loop ...
7
votes
2answers
403 views

How can helicity be conserved but chirality not?

I read in a book that for $\beta$-decay the electrons have always been found to have an expectation value for their helicity of $h=-v/c$. Then ist is said in the book, that it follows from this ...
2
votes
0answers
205 views

Chiral Anomaly in Massless QED

Classical massless QED has axial current conservation. When quantizing the theory, we expect that suddenly $\partial_\mu \hat{j}^{\mu5}\neq0$ (as an operator equality). I have two questions regarding ...
1
vote
0answers
146 views

Chirality of Weyl Semimetal

For Weyl semimetal, the effective Hamiltonian reads: $$H=E_0 \mathbb{1} + v_0 \cdot \mathrm{q} \mathbb{1}+\sum_{i=1}^{3} \mathrm{v}_i \cdot \mathrm{q} \sigma_i$$ Why is the chirality given by ...
7
votes
0answers
940 views

Impostor Higgs?

I recently came across this article, published in the respectable European Physical Journal A. (Apparently, there isn't any corresponding arXiv article for this, so I'm sorry if everyone isn't able to ...
3
votes
1answer
227 views

How can a left-handed fermion field create a right-handed antifermion?

My question - which is likely stupid or appears due to some confusion - stems from the following considerations: when quantizing canonically we are told (see any book on QFT) that a Dirac fermion ...
1
vote
1answer
41 views

Electron indistintinguishability and handedness

I just learned that right ad left handed electrons behave in a remarkably different way under the weak interaction. Up till now I have been told that all the electrons are exact copies of one ...
9
votes
1answer
478 views

What is chirality?

I actually wanted to make the title as "What is the difference between chirality and helicity"? But I didn't do that because I don't understand properly what chirality is. I have gone through this ...
0
votes
1answer
39 views

Behavior of Pion-Mediated Nuclear Force before Electroweak Symmetry Breaking?

When Chiral Symmetry was exact, as it was before EWSB due to the lack of mass terms for quarks, would the residual strong force have infinite range? Related to this, does the Negative Beta Function ...
5
votes
0answers
63 views

Optical chirality and its possible hierarchy of generalizations

Optical chirality refers to a constant of motion of the electromagnetic field, which measures in some sense how chiral a light field is. Specifically, the pseudoscalar quantity $$ ...
14
votes
1answer
259 views

Chirality, helicity and the weak interaction

From what I'm understanding about Dirac spinors, using the Weyl basis for the $\gamma$ matrices the first two components behave as a left handed Weyl spinor, while the third and the fourth form a ...
1
vote
0answers
119 views

How do I prove the equivalence of chirality and helicity operators acting on a massless Dirac spinor?

I have massless Dirac equation and chirality and helicity operators which are given as $$ \hat {P}_{ch}\Psi = \gamma_{5}\Psi, \quad \hat {P}_{h}\Psi = \frac{(\hat {\mathbf S} \cdot \mathbf ...
3
votes
1answer
228 views

How to determine the orientation of the massive Dirac Hamiltonian?

In the calculation of the Chern number within a 2D lattice model, let's take the Haldane model for example, the Chern number$=\pm1$ has 2 contributions coming from 2 Dirac points described by ...
6
votes
1answer
371 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 ...
1
vote
1answer
155 views

Massless neutrinos and Chirality

The massless neutrinos can be represented by two component Weyl spinors. Then how does one say that it is an eigenstate of the chirality operator $\gamma^5$, which is a $4\times 4$ matrix and can act ...
3
votes
0answers
45 views

Mirrored decoupling fermion doublers and a lattice chiral fermion / gauge theory

Nielsen Ninomiya Fermion-doubling problem has known to be a challenge to construct a chiral fermion or chiral gauge theory on the lattice. There is a proposed resolution to use so-called two mirrored ...
9
votes
1answer
205 views

Complex Representation of a gauge group and a Chiral Gauge Theory

In this John Preskill et al paper, a statement is made in page 1: We will refer to a gauge theory with fermions transforming as a complex representation of the gauge group as a chiral gauge ...
4
votes
1answer
464 views

Components of the Weyl spinor field

In the Weyl basis we can separate the spinor field into 2 components: the right-chiral spinor and the left-chiral spinor. Each of these fields has again 2 components which are coupled. What is the ...
4
votes
1answer
234 views

Chiral Spin Liquid(CSL), Chern number, and the ground state degeneracy(GSD)

Consider a 2D gapped CSL with a nonzero Chern number $m$, then is the GSD of the system on a torus directly related to the Chern number $m$? For example, see this article, in the last paragraph on ...
4
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1answer
123 views

Ground states of Chiral Boson Theory with tunneling

I am reading this paper(pdf) and on page 11, the chiral boson theory on a cylinder is studied when both edges of the cylinder are brought in close proximity so that electron is allowed. Why is it ...
3
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3answers
1k views

Why does the Standard Model predict Neutrinos are massless?

Why are neutrinos massless in the Standard Model? Is it connected with experimental fact that neutrinos always have only one direction of projection of spin on motion direction?
8
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1answer
886 views

Explaining chirality for spin 1/2 particle

I found the following explanation for chirality for spin 1/2 particles here What happens when you rotate a left- vs right-chiral fermion 360 degree about its direction of motion. Both ...
3
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1answer
283 views

Definition for Chiral Spin Liquid

What is the definition of chiral spin liquid? Especially what does chiral mean here? I encounter a lot of terminologies with chiral. It seems they mean differently in different contexts. If you could ...