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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Particles physics - Projection matrices

I'm struggling with a question were I'm asked to simply the following expression such that my result only involves one projection matrix. $$P_L \not p \not k P_L $$ Where $$P_L = (\frac{1-\gamma_5}{2})...
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Penrose's consideration of the electron's chirality as “Zitterbewegung”

In his book "The Road to Reality" chapter 25.2 Roger Penrose describes the motion of an electron as a permanent change of helicity states in form of a zig-zag. He takes the Dirac-equation in ...
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$SU(5)$ GUT Yukawa couplings

How exactly in $SU(5)$ GUT a coupling of fermions with different chiralities to the corresponding scalar fields is realized? The yukawa coupling in general form is $\bar5_FY_510_F5^*_H+\frac{1}{8}...
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Particle Physics: Decomposition of a Helicity Spinor

I would have a general question: If we consider the decay of the $W^{-}$ boson into $l^{-}\nu_{\bar{l}}$, how can we calculate the polarization of the $l^{-}$?For example, Mark Thomson has on page 299,...
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Chiral symmetry

Where can I find Information on how electrons have chiral symmetry only if the massless and how it is broken by electron mass correction term? Everything I keep reading seems to be to do with quark's ...
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What intuition led to J. Wang and X.G. Wen's lattice formulation of the 3450 chiral gauge theory?

In the paper cited below, Juven Wang and Xiao-Gang Wen give an example of a lattice model that reduces to a chiral $U(1)$ gauge theory at low energy. The low energy theory is called the $3450$ model. ...
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If you travel faster than a neutrino, will it appear right-handed?

Since neutrinos have mass they move slower than lightspeed. So it is possible to move faster. And if you move faster than the relative direction of the neutrino velocity is backwards. But the spin ...
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Chiral symmetry in Su-Schrieffer-Heeger (SSH) model

We know that the hamiltonian SSH model in the presence of on-site potential(V) can be written on the basis of the Pauli matrix. $$h(k)=V\sigma_0+h_x\sigma_x+h_y\sigma_y,$$ and the term V breaks the ...
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Transformation Properties of the Cross Product

In Goldstein's Classical Mechanics, the cross product $\mathbf{V}^{*}$ of two vectors $\mathbf{D}$ and $\mathbf{F}$, with components $D_i$ and $F_i$ with respect to some Cartesian reference frame, ...
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Calculations of chiral condensate (from David Tong's notes)

I got confused on the calculation of chiral condensate in David Tong's Gauge theory. The equation 3.52 reads \begin{equation} \langle\bar{\psi}_{-}\psi_{+}\rangle=\big(\prod_{n}\lambda_n\big)\frac{1}{...
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Does chirality of electron beam change in a magnetic field?

I'm trying to understand spin. If I have a beam of electrons near the speed of light such that a detector would say they are mostly left-handed. Then I pass them through a magnetic field which rotates ...
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Positron decay direction from muon

I read that in the rest frame of a positive muon, decay positrons are preferentially emitted in the direction of the muon spin. Why is that the case? The decay is $\mu^+\to e^+\nu_e\bar{\nu_\mu}$. ...
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Confused about SM neutrinos

I am a bit confused about neutrinos in the standard model. The vertex of the weak interaction charged current, implies that any neutrino interacting through the charged current must be left handed. ...
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Chiral vortical effect (CVE) and gravitational anomaly

Chiral vortical effect is a generation of an axial current in the presence of the rotation. On the one hand, the expression for the $\mathbf{CVE}$ has the following form: $$ \vec{J}^{5} = \vec \Omega \...
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String theory allows chiral gauge coupling

In Polchinski String Vol 1: Chiral gauge couplings. The gauge interactions in nature are parity asymmetric (chiral). This has been a stumbling block for a number of previous unifying ideas: they ...
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Could graviton exist in a single polarisation?

Penrose's twistor theory can only construct a left-handed graviton. This is seen as a problem. But... is there anything wrong with gravitons existing in only one polarisation? How would gravity differ ...
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Polarization vector of chiral light

I was curious about the following point: let's say we have a left circularly polarized light wavepacket travelling from left to right. We will call its polarization vector $\epsilon_{L}$ while the ...
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How can tin whiskers be produced?

How can tin whiskers be produced in an easy way as fast as possible without needing temperatures above 100 °C and in atmospheric pressure? Metal whiskers grow from bottom and up. It is not a form of ...
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Conservation of chirality in non-weak elementary particle interactions

Chirality is not conserved in propagation (e.g., electron oscillates between left and right chiral). But is chirality conserved in interactions? What is a good reference paper or book for this notion ...
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What is the action of the field $\Psi_L$ on vacuum?

Please help me to understand the following situation. A fermion field $\Psi(x)$ acting on the vacuum can destroy a particle and create an antiparticle. If however, a chiral field $\Psi_L$ defined as $\...
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Confusion about chiral anomaly (Fujikawa's method)

I am reading Fujikawa's method for calculating chiral anomaly, see this wiki page. The method can be described as follows. It starts with the path integral \begin{equation} Z=\int\mathcal{D}\psi\...
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Effects of the discrete quotient of chiral symmetry group

For a theory of $N_f$ massless Dirac fermions coupled to a Yang-Mills field, the usual story is that we have a $U_L(N_f)\times U_R(N_f)$ symmetry, which is then expressed as $SU_L(N_f)\times SU_R(N_f) ...
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Both formalisms of a chiral multiplet in Supersymmetry

For the description of a chiral multiplet in Supersymmetry there are 2 formalisms, the one I am used to presented for instance in the Supersymmetry Primer of SP Martin which is based on 2-component (...
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Chiral symmetry in massless QCD

The QCD Lagrangian for two flavors is: $-\frac{1}{4} G\tilde{G}+i\bar{u}\displaystyle{\not} D u+i\bar{d} \displaystyle{\not} D d-m_u\bar{u} u-m_d\bar{d}d$ or alternaively $-\frac{1}{4} G\tilde{G}+i\...
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Do the right-chiral electron and left-chiral positron interact with the anti-$W$ boson?

I've been reading Flip Taneda's 'quantum diaries' articles, and he references the famous fact that the W boson (weak force) only interacts with left-handed electrons and right-handed positron. BUT... ...
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Can a right-chiral electron annihilate on contact with a right-chiral positron?

Or, do two particles have to be 'anti' in every sense of the word? (Opposite charge, opposite chirality, etc.) Edit: Just to clarify... Antiparticles can have multiple properties that are 'anti' of ...
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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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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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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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