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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How can the strong nuclear force (QCD) be considered to violate chirality, but not parity?

Chirality is related to parity, correct? It is a form of 'parity'? So, How can the strong force violate chirality symmetry, but only the weak force violates parity symmetry? I am confused about the ...
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Are massless antineutrinos in the Standard Model right-handed or right-chiral?

For massless fermions, their chirality (determining under which representation of the Lorentz group they transform) and their helicity (projection of spin onto three-momentum) eigenvalues are the same....
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Chiral zero modes in type IIB matrix model

I have seen many articles in which the authors consider various modifications of IKKT matrix model (non-perturbative regularization of type IIB string theory) such as (Orbifolds, fuzzy spheres, ...
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Explanation of some physical terms related to hydodynamic limit to a non-physicist & Integrable system

I'm a mathematician, and I'm reading an article and am struggling with some of the terminology related to physics. [...] This equation is formally obtained from the hydrodynamic limit of the ...
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Are there non-lagrangian field theories for massive Weyl spinors?

It is a well-known fact that a chiral fermion is massless, since the mass term involves both a right-handed and a left-handed field. If you have one chirality only there are no mass terms one can ...
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Mass term in chiral lagrangian and chiral lagrangian

Mesons in chiral lagrangian are described by the chiral action $U = e^{2i\pi^a T^a/f_\pi}$, \begin{equation} \mathcal{L}_{chiral} = \frac{f_\pi^2}{4} \text{Tr} \left( \partial^\mu U^\dagger \...
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A question involving chiral transformations and gamma matrices

I'm looking at a calculation that involves an infinitesimal transformation of a Dirac fermion field: $$\Psi \rightarrow e^{i \beta \gamma^5} \Psi.$$ Then the conjugate field $\bar{\Psi} = \Psi^{\...
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Are there physical reasons for breaking this symmetry in biological systems?

For some reasons, it seems that particular "handedness" are chosen by nature, because we have the prevalence of some enantiomer, that have different optical properties respect to ...
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Confused about chirality of antiparticles and QED interaction

In the middle of doing some calculations and I seem to have forgotten some basics from QFT. I would be very grateful if someone could help me out! Taking, for example, an interaction proportional to $\...
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With a local anomaly, is the determinant of the Dirac operator still a section of a complex line bundle?

In the literature about anomalies in quantum field theory, the determinant of the Dirac operator plays an important role. The Dirac operator may depend on some background data, and the subject of ...
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Confusion with helicity eigenstates of massless spinors

As presented in Schwartz´s QFT and SM one can solve the free Dirac Equation in the Weyl basis. If $p^{\mu} = (E,0,0,p_z)^T$ the four solutions are: \begin{equation} u_1^p = \begin{bmatrix} \...
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Can a QFT be anomaly-free on spacetimes that are boundaries but still have an anomaly on other spacetimes?

If $D$ is the Dirac operator for some dynamic spinor fields in background gauge and gravitational fields, then the partition function is supposed to be $\mathrm{det}(D)$. For this to make sense, we ...
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Anomalies in QFT: why do we require smooth dependence on the background fields?

If $D$ is the Dirac operator for some dynamic spinor fields in a background gauge field $A$, then the partition function is supposed to be $\mathrm{det}(D)$. But if the coupling to the gauge field is ...
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Were electrons initially left-handed, as neutrinos still are today?

These days, neutrinos are left-handed, just as they were a long time ago. These days electrons are right- as well as left-handed. Were they only left-handed a long time ago, before having interacted ...
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Chiral Fierz identity

I am having trouble with proving the following: $$(\bar{\psi}_1 P_R \psi_2) (\bar{\psi}_3 P_R \psi_4)=-1/2 (\bar{\psi}_1 P_R \psi_4)(\bar{\psi}_3 P_R \psi_2)-\dfrac{1}{8}(\bar{\psi}_1\sigma_{\mu\nu} ...
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Srednicki Chapter 83--Flavor symmetry change going from global $U$ symmetry for color group $SU(3)$ vs. $SO(3)$

I am writing about the first homework question in Srednicki Chapter 83 (83.1 part a). Please help me check my understanding. In other words, would my reasoning below be right? Forgive me too if ...
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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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