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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Magnetoelectric effect

I am trying to find a concise and clear paper/book/reference in which there is a proof of the fact that any chiral molecule shows magnetoelectric effect. Could someone help please?
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How can higher-energy beta decays have 'higher polarization'?

The higher the energy of the particles, the higher their polarization. I just cut-and-pasted the above statement from the chirality-and-helicity section of the Wiki article on 'Beta decay'. What does ...
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Goldhaber experiment - Why are there only left-handed neutrinos?

"From the Goldhaber experiment we can deduce that there are only left handed neutrinos." I don't understand this. Can't we find an experiment that only produces overwhelmingly right handed ...
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Annihilation cross-section of neutrino-antineutrino pairs [duplicate]

Presumably this should be a tiny cross-section (or not?), but presumably it should be at least qualitatively similar to the 511 keV line that clearly distinguishes electron-positron annihilation, ...
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Explicit Symmetry Breaking in Chiral Lagrangian

Currently I am going over explicit symmetry breaking in chiral Lagrangians. In particular, consider a term \begin{equation} \mathcal{L}_{\text{mass}} = \bar{Q}MQ \end{equation} where $Q = (u, d)^T$ ...
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Conservation of left-handed quark current

I'm reading about the Operator Product Expansion in Gelis's A Stroll Through Quantum Fields section 7.4.2. As an example, he's using the product of currents $$A_1^\mu = \overline{d}_L\gamma^\mu u_L$, ...
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Dirac equation solution - four-component spinors - left-/right-handed in ultrarelativistic limit

I am confused about the solution to the Dirac equation and how it corresponds to left-/right-handed Weyl spinors. In Srednicki, page 242, it is stated that taking the ultrarelativistic limit ($|\bar{p}...
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Chiral anomaly in Weyl semimental

In Weyl semimetal, there is an analog of ABJ anomaly, which is a $E \cdot B$ term. The ABJ anomaly can be viewed as winding number because of the homotopy group of sphere $\pi_3(S^3)= \mathbb{Z}$ for ...
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Chiral anomaly for massless Dirac fermion

Let us assume we have a single flavor massless Dirac fermion with Lagrangian $\mathcal{L} = \bar{\psi}i\gamma^{\mu}D_{\mu}\psi + \mathcal{L}_{gauge}.~$ Due to chiral anomaly, chiral symmetry is not a ...
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Among free quantum field theories, do all 't Hooft anomalies arise from chiral fermions?

In quantum field theory, a global symmetry group that can't be gauged is said to have an 't Hooft anomaly. One of the most familiar examples is the free massless Dirac fermion in $3+1$ dimensional ...
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Definition of 'Antichiral' in the Thirring Model

This is my first post on this website so please excuse any poor formatting. In the lecture series on quantum integrable models, much attention is focused towards the Thirring model, $$\mathscr{L} = \...
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Helicity and chirality of particles in the pion decay

Let us consider the $\pi^+$ decay: $$\pi^+(q) \rightarrow \nu_\mu(p_1) + \mu^+(p_2)$$ In the Standard Model, the neutrinos are left-handed. Since they are massless, chirality corresponds to helicity. ...
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What are differences among chiral, helical and spiral in quantum spin context?

For chiral, as far as I know, there are vector chirality $\kappa_{ij}=\mathbf{S}_{i}\times \mathbf{S}_{j}$ which characterizes non-collinear spin arrangement and scalar chirality $\chi_{ijk}=\mathbf{S}...
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Apparent coincidence of spin-connection term and Higgs field?

In curved space time, there is a spin-connection term $\overline{\psi}\gamma^\mu\sigma^{ab}\omega^{ab}_\mu\psi$. Here's my apparent problem. If there were no Higgs field and no gravity, all particles ...
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Conservation of the axial current using Dirac equations of motion

Dirac equation: $$(i\gamma^\mu\partial_\mu -m)\psi=0$$ implies $$\gamma^\mu\partial_\mu \psi=-im\psi$$ Adjoint Dirac equation: $$(i\gamma^\mu\partial_\mu +m)\overline{\psi}=0$$ implies $$\...
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Show that $\nu^c _L = (\nu ^c)_R $

Considering Majorana neutrinos, how can I show that $\nu^c _L = (\nu ^c)_R $? I don't know how to answer this question. And what is the difference between $\nu ^c _R $ and $(\nu ^c)_R $? I know it ...
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Why do we know that the right-handed electrons exist?

I am wondering how come Weinberg and Salam put the right-handed electrons and did not put right-handed neutrinos* into the theory? In other words, are there any experimental/theoretical indications ...
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Relation between chiral symmetry and chiral material

There seems to be two types of chiral. One chiral is usually referred to in terms of chiral symmetry or its breaking. It can be in the context of field theories where mass generation mixes left &...
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What do you mean by in the mirror world?

I was trying an attempt to replicate Wu experiment mentally when I heard the term mirror world kept popping ups, why should we care what happens inside the mirror world? Is it a math thing?
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Number of Weyl points due to symmetries

In Weyl semimetals time reversal symmetry (TRS) or centrosymmetry has to be broken (CS). It is stated, there are at least four Weyl points in TRS systems. I tried understanding this looking at the ...
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Is there an anisotropy factor (g factor) for TDDFT Abs and CD calculations?

Experimentally, anisotropy factor is calculated by dividing the CD spectra by the absorbance spectra multiplying by a factor of 32980 (in order to get a nondimensional quantity) Theoretical ...
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Chiral elastic solids

Equations in these two pictures are similar, but in the second pictures, the author set the C1, C2 of the equations to be zero and get the final equation shown in picture 2 My question is why the ...
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Dirac Lagrangian in terms of left and right handed fields

When we define the operators $P_{L,R}=\frac{1\mp\gamma_{5}}{2}$, we are able to define right- and left-handed Dirac fields: $$\psi=(P_{L}\psi+ P_{R}\psi)=:\psi_{L}+\psi_{R}$$ The corresponding Dirac-...
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Quark Chirality Constraints in Nucleons

SW Engr here educating myself on particle physics, apologies in advance for any phrasing errors. I tried the google machine to no avail. Q: If only left handed matter fermions experience the weak ...
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A very naive question about Weyl spinor

Suppose we consider a left-handed Weyl spinor. Is its anti-fermion right-handed or still left-handed?
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Dirac spinor and Lorentz group

How does the reducibility of lorentz group ensures that there exist two types of particle i.e left-handed and right-handed (weyl spinors)?
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Are right-handed chiral particles more stable than left-handed?

Are right-handed chiral particles usually more stable than left-handed because right-handed particles can't decay using W⁺/W⁻? For example, left-handed muons apparently decay most of the time in such ...
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The spin of light

The so-called spin is circular polarization of light,that is the electric field rotates in either direction normal to propagation Is it known or is there any theory about how fast the field rotates? ...
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Why chirality leads to stable gapless modes?

It is known that some topological orders in 2-D exhibit chiral edge modes. I am just wondering how the statement of chirality relates to its spectral property of gapless. I`ve heard things like 'back-...
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If I attach two leads at the edge of a quantum hall system, can I get the current without adding voltage difference between the two leads?

In a 2-dimension quantum hall system, there always exist the chiral edge state in one edge. The current of the edge state is always in one direction, e.g $v_x>0$. In this case, if I attach a ...
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Peskin's treatment of Pions as Goldstone Bosons

After restoring the mass terms in the Lagrangian \begin{align} \mathcal{L}=\bar{u} i \not D u+\bar{d i} \not D d-m_{u} \bar{u} u-m_{d} \bar{d} d, \end{align} one obtains equations of motion for the ...
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How can we interpret the components of a polarization four-vector?

The four components of a Dirac spinor can be interpreted in terms of left-chiral and right-chiral spin up and spin down states. How can we interpret the four components of a polarization four vector $...
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Why do quarks flip chirality when exchanging an instanton?

Quarks are elementary particles, part of the SM. There are a lot of different questions and answers on this site about chirality, I did not find a really good description, so I will use this wiki ...
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Chiral anomaly: gauge covariance and regularization

I am looking at the treatment of the chiral anomaly in Fujikawa and Suzuki's "Path Integrals and Quantum Anomalies." To illustrate the quantum breaking of chiral symmetry (section 4.3), they start ...
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Difference between left- and right-handed, helicity and chirality

What is the difference? I know there is the (almost) same question What's the difference between helicity and chirality? but when a particle is given as left-handed. Is it helicity or chirality?
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Almost complex structure $J_i^j$ from covariantly constant spinor $\eta$

In the context of superstring compactification on a 6-manifold which admits a covariantly conserved spinor $\eta$, which we normalize so that $\eta^{\dagger} \eta = 1$, I am trying to show that the ...
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Why does the majorana equation preserve handedness?

In the "QFT Nutshell" by A. Zee, it is stated that The Majorana equation is $$i\not\partial\psi=m\psi_c$$ where $\psi_c$ is the charge conjugated spinor $\psi_c = \left(C\gamma^0\right)\psi^*$....
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Free fermion Lagrangian invariance under chiral symmetry

I want to apply this transformation to a free-fermion lagrangian: $$ L=\bar{\psi}(\gamma^\mu{\partial_\mu \,- m)\,\psi}$$ $$ \psi ' =\psi\; e^{i \alpha \gamma_5} $$ $$ \bar{\psi}'=\bar{\psi} \;e^{-i \...
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Sufficient and Necessary Conditions for Chiral Symmetry Breaking

In their 2005 paper, the authors write (just below eq. 3.19) we see that a non-zero value of $F_0$ is a necessary and sufficient criterion for spontaneous chiral symmetry breaking. On the other ...
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Weak hypercharge physical existence

How do we know that electrons are chiral? Even if left-handed electron carries weak hypercharge, it's only for an infinitesimally small time or is it predicted by QFT?
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Embedding of $SU(2)_L \times U(1)_Y$ into $SU(2)_L \times SU(2)_R$ in electroweak chiral effective theories

In the context of chiral effective theories we usually deal with the pion field \begin{equation} U= ie^{\frac{\pi^a \sigma^a}{2f}} \end{equation} where $\pi^a=\big(\pi^1, \pi^2, \pi^3\big)$ are the ...
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Massive chiral fermions

The main question is: why does nobody care about massive chiral fermions? It is well-known that in QFT (in the axiomatic framework of Garding & Wightman) the quantum field transform according (...
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EW theory vertices

I'm trying to undertand the following vertex: Initial state of up and anti-down quarks with finalk state made of $W^+$ boson. Does it go with left or right projector? I think that from Lagrangian it ...
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How to determine the squared average amplitude for $\nu_e(p_1)+d(p_2)\rightarrow e^-(p_3)+u(p_4)$?

I have the following charged current interaction, at quark level, by the process: $$\nu_e(p_1)+d(p_2)\rightarrow e^-(p_3)+u(p_4)$$ By assuming that the energy is such that I can neglect the lepton and ...
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Can neutrinos change chirality by oscillating?

Active neutrinos are left-handed while sterile neutrinos are right-handed. There are speculations that active neutrinos can oscillate into sterile neutrinos. Can neutrinos change chirality by ...
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Left Handed / Right Handed Particles and the Weak Force

Good Afternoon, I am a 50-year-old guy who was never a scientist or physics student. Just a person who loves to read books on particle physics. I have a question on the Weak Force and particles. (...
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Nielsen-Ninomiya Theorem versus Chiral Gauge Anomaly

As far as I understand, the Nielsen-Ninomiya theorem states that (under mild conditions) the number of left and right-handed chiral fermions must be equal on the lattice, while the chiral gauge ...
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Meaning of the subscripts $L,R$ for the two component Weyl spinors $\phi_{L,R}$

For a Dirac spinor $\psi$, its chiral projections are $\psi_{L,R}$ are defined as $$\psi_{R,L}=\frac{1}{2}(1\mp\gamma^5)\psi.\tag{1}$$ Acting with the chirality operator $\gamma^5$, we find $$\gamma^5\...
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Energy difference between enantiomers (matter/antimatter)

I am aware of the fact that enantiomers have different energies, for example L-amino acids have different energy than D-amino acids. The difference is not significant and is most usually about $10^{-...
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How a moving electron gets deflected in a magnetic field in on direction and the positron gets deflected in the opposite direction? [duplicate]

In a question Why does nature prefer the right-hand rule over the left-hand rule? was another question My question is, why this direction and not the opposite? This part of the post received no ...