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2
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0answers
38 views

Conceptual interpretation of the left- and right-handed spinor representations of the Lorentz group

I understand mathematically that the Lorentz group's Lie algrebra $\mathfrak{so(3,1)}$ (given by eqns. (33.11)-(33.13) in Srednicki's QFT book) is isomorphic to $\mathfrak{su(2) \times su(2)}$ (given ...
0
votes
1answer
32 views

How do quarks interact with the higgs field

I know that electrons' only interaction with the higgs field is due to ambidextrousness and the weak hypercharge which is provided by the higgs boson, but how do quarks (specifically up and down) ...
0
votes
0answers
21 views

Pion decay from chiral anomaly

I have to compute the decay rate of the process: $$ \pi^{0} \rightarrow \gamma \gamma $$ with 4-momenta $P \rightarrow K_{1}+K_{2},$ by the means of the following effective Lagrangian, coming from ...
2
votes
0answers
36 views

Physical meaning of the chiral condensate in QCD

Considering the QCD Lagrangian in the chiral limit, where all the quarks masses are set to zero. Then the Lagrangian has the following chiral symmetry: $$ SU(L)_{V} \times SU(L)_{A} \times U(1)_{V} \...
4
votes
1answer
163 views

Two conflicting definitions of chirality

Consider a Majorana fermion embedded in a Dirac spinor, $$\psi = \begin{pmatrix} \psi_L \\ i \sigma_2 \psi_L^* \end{pmatrix}.$$ The Majorana fermion $\psi_L$ is left-chiral, i.e. it transforms in the ...
1
vote
1answer
58 views

Preference of Chirality

I was interested to see that , $$ \gamma^5 \psi = \psi_R - \psi_L $$ By the definition of chirality projection operator and that $\psi = \psi_R + \psi_L$. since $\gamma^5 \psi$ pops up a lot in QED,...
3
votes
1answer
83 views

Confusion with chirality eigenstates

In the Weyl/chiral basis, the four components of the Dirac spinor represent left-chirality spin up, left-chirality spin down, right-chirality spin up, and right-chirality spin down, respectively. When ...
3
votes
1answer
100 views

Can I catch a particle (such as electron) and say it's left hand

Why is only the left hand electron coupled to weak interaction? How can I tell the chirality of an electron?
3
votes
1answer
91 views

How can neutrinos have both mass and helicity?

If a neutrino has mass it must travel at less than the speed of light. So how can it possess helicity, which can change depending on relative velocity?
3
votes
1answer
71 views

If a neutrino and his antineutrino has different helicity how can it be a possibility that it is a Majorana particle?

All antineutrinos observed thus far possess right-handed helicity (i.e. only one of the two possible spin states has ever been seen), while neutrinos are left-handed. Notwithstanding that it is said ...
1
vote
1answer
72 views

Why only left-handed neutrinos have been observed yet?

This is what I understood (it may be wrong, so please correct me): since every particle is "divided" into a lefthand and a righthand partner, which is what guarantees the particles to have mass, and ...
2
votes
1answer
37 views

Weak isospin transformation of $\bar\psi \psi \phi$

In an old exam I found the following question regarding the Higgs potential: Write down the gauge invariant Yukawa interaction term in the Lagrangian that gives rise to the electron mass. The ...
2
votes
2answers
71 views

Chiral symmetry breaking and confusion with terminology

I am confused about Chiral symmetry breaking and the terminology we use. First of all, I think the symmetry is started with taking quark masses zero and writing the Lagrangian as; $$ L=-\frac{1}{4}(F_{...
1
vote
0answers
18 views

Chiral tunneling in Weyl Equation

I am trying to understand perfect tunneling of particles obeying Weyl equation through a potential barrier at normal incidence. I know that this has something to do with chirality, but I am not ...
1
vote
1answer
131 views

What is polarisation, spin, helicity, chirality and parity?

Polarisation, spin, helicity, chirality and parity keep confusing me. They seem to be related, but exactly how they are related is unclear to me. Can someone maybe give a short overview about what ...
11
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1answer
298 views

How do higher-order optical chiralities look like?

The optical chirality of the electromagnetic field is a conserved quantity, analogous to the energy density, linear momentum density, and angular momentum density, which describes how chiral the EM ...
2
votes
1answer
76 views

Chiral current VEV below the QCD scale

Let's have pure QCD. I know that after spontaneous symmetry breaking quark bilinear form are replaced by their averaged values: $$ \bar{q}_{i}q_{j} \to \langle \bar{q}_{i}q_{j}\rangle \approx \Lambda_{...
3
votes
0answers
52 views

How does one determine chirality experimentally?

The Standard Model says that only left-handed electrons participate in weak interaction. A very natural question for novices like me is then: How can we tell, experimentally, if an electron is left-...
0
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0answers
48 views

Could the gauged six-dimensional chiral supergravity model explain dark matter, as well as gravity?

I was reading a paper on 6-dimensional supergravity http://www.math.ist.utl.pt/~strings/MTST2/audio/pope1.pdf after watching a sixty symbols video on it https://www.youtube.com/watch?v=O4eXU8VHM2g ...
7
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0answers
83 views

Distinguishing between left-handed and right-handed weak coupling from electron-neutrino scattering

This question comes from Schwartz's QFT book, exercise 13.6. In it we consider a coupling between fermions (neutrinos and electrons in this particular case) and the Z boson of the form $g_V \bar{\psi} ...
1
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0answers
35 views

Massless Dirac Field Chirality and CP

I have some very basic questions about Quantum Field Theory. So let's assume we have massless fermions. In 4 spacetime dimensions, due to the Group Structure of $SO(3,1)$ there exists the famous $\...
3
votes
1answer
116 views

Is there a bulk signature of topological nontriviality for a 3D free fermion band insulator?

Is there such thing as a 3D Chern invariant (or some other quantity) that I can use to test an insulating quasiparticle spectrum is a topologically trivial or non-trivial insulator? Does one exist ...
2
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0answers
39 views

Vector mesons as background gauge fields

Suppose we have some complicated fundamental theory of fermions and gauge fields which involves global chiral symmetry and global anomalies which breaks some subgroup of this symmetr. At some energy ...
0
votes
0answers
40 views

Simple question about gamma five and re-writing the Dirac lagrangian

I'm working a problem (Zee, p. 100) asking me to rewrite the Dirac lagrangian in terms of the left and right projections, and along the way I run into: $$\overline{\psi} i \gamma_µ \partial^µ \psi - \...
2
votes
2answers
106 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 ...
5
votes
1answer
394 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
66 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 ...
2
votes
2answers
156 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 the ...
2
votes
0answers
88 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. ...
5
votes
2answers
178 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
109 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
186 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
55 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 $U(2)...
1
vote
1answer
225 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
110 views

Why would a square matrix transform?

Why would a square matrix of spinless fields $\Lambda$ transform under symmetries? Given: $$\delta \psi_L = i \epsilon_L^aT_a\psi_L$$ and $$\delta \psi_R = i \epsilon_R^aT_a\psi_R$$
1
vote
0answers
42 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 ...
7
votes
1answer
270 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 ...
4
votes
1answer
163 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
19 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 ...
7
votes
5answers
473 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
159 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 ...
5
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2answers
1k 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 ...
11
votes
3answers
580 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
159 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
482 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
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0answers
58 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
6
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0answers
351 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
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1answer
745 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
172 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 \bar{\Psi}...
3
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0answers
73 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 ...