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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Spinor Components, Helicity, and Chirality in Dirac Theory

In the Dirac the spinor components are defined by fermion/antifermion (here labeled as $+,−$) and spin component $S_z$ ($↑,↓$): \begin{pmatrix} \psi_-^\uparrow \\ \psi_-^\downarrow \\ \psi_+^\uparrow \...
Julián Oviedo's user avatar
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Can an electromagnetic wave be polarised in the direction it propagates?

Can the electric field vector of an EM wave oscillate in the propagation direction? In text books the polarisation is always orthogonal to the propagation direction. I'm wondering specifically ...
Jorge's user avatar
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Isn't linearly polarised light actually chiral or am I stupid?

Isn't linearly polarised light actually chiral when taking the magnetic field into account? Just looking at the electric field is just 2D and therefore achiral, obviously. But with the magnetic field ...
Jorge's user avatar
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How are chiral bosons defined?

What is the definition of chiral bosons? Until now I only knew the derivation of the chiral fermions (used in the Dirac field equation).
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Does the number of right chiral neutrinos always need to be the same as the number of anti left chiral neutrinos?

Neutrinos are only observed to have a left handed chirality and anti neutrinos are only observed as having a right chirality. In some beyond the standard model hypotheses neutrinos of right chirality ...
The Burger King's user avatar
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Massless limit of the Dirac theory

What is the physical reason why there is no mixing between left-handed and right-handed Weyl spinors in the massless case of the Dirac theory? Why does the chirality of a massive particle change ...
Michael's user avatar
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Physical significance of left- and right-handed spinors

We know that the $(1/2,0)$ and $(0,1/2)$ representations of Lorentz group represent the left- and right-handed spinors respectively. What’s the reason behind this nomenclature? What they represent ...
Sagar K. Biswal's user avatar
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Feynmann diagram for $W$ boson decay

So a $W^{-}$ boson decays into right-handed antineutrino and left-handed lepton with "wrong" helicity. I found that textbook explanation of that process involves lots of handwaving. I am ...
haael's user avatar
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Understanding notation in $-\overline{U}_LmU_R+\text{h.c.} =-\overline{U}mU$

Suppose $U$ is a field with left handed and right handed parts $U_L,U_R $, respectively. When discussing Lagrangians, I keep finding the following simplification step $$-\overline{U}_LmU_R+\text{h.c.} ...
Fernando Garcia Cortez's user avatar
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Is quantum spin intrinsic, or a function of some other characteristic? [closed]

In my current understanding, I have been told that the spin of quantum particles is simply intrinsic to them. That, particles are simply right-handed or left-handed... just because they are. To me, ...
blacktopshaman's user avatar
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Fields as Lorentz group irreps, spin and motion equation

My question touches quite a vast subject. I'm looking for a macroscopic answer without a lot of math, just the one needed to feel the answer. We have $SO(3,1)$ lorentz group, we can give him all the ...
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Trying to derive chiral anomaly in 2D from Feynman diagrams in position space

Trying to understand the Chiral anomaly, I decided to explore the simplest example of a holomorphic fermion in 2D in a background electromagnetic field $A\text{d}z+\bar{A}\text{d}\bar{z}$. The ...
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Can we determine the polarization of a neutrino?

I recently read that neutrinos have a polarization property---their polarization is opposite to antineutrinos. Is it possible to determine the polarization of a neutrino? For example, we can determine ...
Andrew Baker's user avatar
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How is the chirality for the weak interaction conserved for non-relativistic neutrinos?

In this article, one can read that the neutrinos in the cosmic neutrino background have a speed of about 1/50 of the speed of light, which is clearly non-relativistic. From the viewpoint of, say, ...
Il Guercio's user avatar
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Higgs Boson and Chirality

I have seen some statements that the Higgs boson is not responsible for particles gaining mass, but rather the Higgs field is. However, as I understand it, the Higgs boson is just an excitation in the ...
18th Shard's user avatar
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The chirality of the standard model fermions

I read 'The Standard Model Effective Field Theory at Work' by Isidor, Wilsch, and Wyler. In a footnote, they say that, in principle, right-handed neutrinos could be included in the Standard Model by ...
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Interactions in nonlinear chiral theories

When discussing nonlinear realizations of $SU(3)_L \times S(3)_R$ in Chiral theories, it is usual to introduce the interactions between the baryon octet ($B$) and some meson matrix $M$ as \begin{...
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Chiral transformations

In Gerard Ecker's book 'Chiral Perturbation Theory' he states that if we have a symmetry group $G$, an element $g \in G$ induces a transformation in $u \in G/H$ \begin{equation}\tag{1} u(\phi) \...
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Can you tell wavefunction's chirality by looking at it?

I recently learned, that: Helicity is a combination of particle's "rotation" (Spin) and direction of it's motion. The motion is relativity-dependant, and so is helicity. Chirality ...
Victor Novak's user avatar
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Mass as generator of two distinct sets of phenomena

We know that mass, which is a continous parameter, generates two classes of different phenomena: the ones where $m=0$ and the ones with $m \neq 0$. When a particle has $m=0$ we have phenomena which ...
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Why do we not use SI units for optical rotation of substances in solution?

This question is with regards to a polarimetric approach in analysing the concentration of a substance in solution such as sugar in water. I have been trying to find an answer to it through a little ...
Thomas Shelby's user avatar
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Chirality flip in electrons due to Yukawa interaction

This is the Lagrangian density for a fermions interacting with a Higgs field: $$\mathcal{L}= i \bar{\Psi} {\gamma}_\mu {\partial}_\mu \Psi - (gv) \bar{\Psi} \Psi + \frac{1}{2} {(\partial h)}^{2} - \...
Julián Oviedo's user avatar
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Chiral Lagrangian Field

In the chiral model $SU(N)_R × SU(N)_L$ with gauged Left-handed $SU(N)$, we take as the field the $SU(N)_L$-valued $\Sigma (x)$, defined as $$\Sigma(x) = \exp\big( \frac{2i}{v} \chi^a(x)T^a\big).$$ ...
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Charge+Parity operator lead left-handed to right-handed

So i need to show that the, if $\psi$ is left-handed, $$C\gamma^0\psi^*$$ Is right-handed. So, we know that, for any $\psi$, $P_L \psi$ is left handed. Also, for any $\omega$, is right-handed, $P_R \...
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Antimatter structures and chirality

I'm curious whether the reversal of spin number in antiparticles vis-a-vis their matter counterparts would have a corresponding reversal of the chirality of structures made of antimatter (over scales ...
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How can neutrinos be solely left-handed if they have mass?

Helicity: projection of spin onto motion. Since neutrinos are massive, I can always move to a reference frame where their motion is towards the opposite direction, meaning I should reverse their ...
TrentKent6's user avatar
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Does particle parity play any role in matter anti-matter annihilation?

If a left handed electron and a right handed antimatter electron were to meet, would they still annihilate? In the same way, if a left handed electron and a left handed antimatter electron meet, will ...
NonPartisanObservor's user avatar
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Fermion parity vs gauge symmetry

Take for instance a 4d gauge theory with a fermion $\psi$ in some representation of the gauge group $G$ and say that I want to study the fate of the "non ABJ-anomalous" part of the axial ...
BisonRavi's user avatar
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Experimental distinction between neutrinos and antineutrinos

How can we experimentally distinguish left-handed neutrinos from right-handed antineutrinos when we do not know a priori their creation process (for example in the case of cosmological neutrinos)?
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How does changing handedness cause mass?

I am a very beginner when it comes to the Higgs mechanism, so the best my brain could understand (without the gory math) is the fact that the Higgs field causes fermions to flip between their left- ...
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$\mathbb{Z}_2$ symmetry of 2d Majorana fermion theory

I'm reading A Web of 2d Dualities: Z2 Gauge Fields and Arf Invariants, and confused by a simple statement: the Euclidean kinetic action is invariant under a $\mathbb{Z}_2$ symmetry, while the mass ...
user31415926's user avatar
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$U(1)_A$ axial anomaly for $SU(N)$ gauge theory in 1+1 dimensions

In massless Abelian gauge theory in 1+1 dimensions, the divergence of axial current is given by \begin{align*} \partial_\mu j_A^\mu=\frac{e}{2\pi}\epsilon^{\mu\nu}F_{\mu\nu}=\frac{e}{\pi}F_{01}. \end{...
Kitchen's user avatar
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Chirality of quantum spin

Is quantum spin chiral? If the answer is yes, then we can have four possibilities of quantum state in one direction of measure: Leftie pointing Up, leftie pointing Down, righty pointing Up, righty ...
user61253764's user avatar
2 votes
2 answers
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How is the property of chirality used?

I was studying the book "Scattering and Structure" by Bogdan Povh; it mentions that this property is used as a criterion to decide whether one is dealing with a massless or a massive ...
Kadija's user avatar
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What is meant precisely, when a term in the Lagrangian is "chirally invariant"?

I am reading this paper, where eq. (2): $$ m_0(\bar{\phi}_{-L}\phi_{+R}-\bar{\phi}_{-R}\phi_{+L}-\bar{\phi}_{+L}\phi_{-R}+\bar{\phi}_{+R}\phi_{-L}) \tag{2} $$ is said to be chirally invariant. Here, ...
Polarized photon's user avatar
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Chirality in muon decay

Consider the muon decay process: We assign the chirality according to the $W$ boson current: (i.e. P&S eq.(20.80)) $$J_W^{\mu+}=\frac{1}{\sqrt{2}}\bar{\nu}_{\mu L}\gamma^{\mu}\mu_L \quad J_W^{\mu-...
Daren's user avatar
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How does the factor $m_b$ arise in the weak effective operator $\mathcal{O}_7^\gamma$?

According to [1] one of the dominant operators contributing to the decay $B \rightarrow K^{(*)} \ell^+ \ell^-$ is given by $\mathcal{O}_7^\gamma$. When calculating the coefficient of this operator ...
rgba's user avatar
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Chiral transformation of lattice fermionic operators

Consider the Hamiltonian of interacting particles on a lattice, e.g. the Hubbard Hamiltonian $$ H = -t \sum_{i\sigma} ( c_{i,\sigma}^{\dagger} c_{i+1,\sigma} + \mathrm{h.c.} ) + U\sum_i n_{i\uparrow} ...
Matteo's user avatar
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Explaining "Left" and "Right" to an Alien using Chirality and Helicity

my professor told us that we could hypothetically explain the concept of "Left" and "Right" to a Martian (an alien, etc.) using the fact that Helicity is invariant under parity. ...
Andrea Di Pinto's user avatar
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When we talk about the helicity of a particle, why are we (apparently) ruling out the cases of the spin being perpendicular to the motion direction?

If I assume the (linear) momentum is in the direction of the X-axis, could I NOT find the spin-up in the positive Y-(or Z-) axis and the spin-down in the negative Y-(or Z-) axis?
Minn Htutkyaw's user avatar
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Spontaneously Broken Approximate Symmetry, Weinberg 19.4, QFT 2

I am having difficult time understanding part of 19.4 section where Weinberg introduces the symmetry breaking terms for $SU(2)\times SU(2)$ symmetric theory for $u,d$ quarks, specifically, he adds (eq....
physicsbootcamp's user avatar
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Prove that Majorana mass term is Lorentz invariance

I have a homework to prove that using one kind of chirality, let's say left-handed, we can construct a mass term. The argument is to show that this term $\psi^TCP_L\psi$ is satisfy the dimensionality ...
Den Jaka's user avatar
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On weak interaction and right-handed particles

The weak interaction involving $Z^0$ boson has the following expression for its current: $$ g_{\rm{z}}J_\mu^Z = \frac{g_{\rm{w}}}{\cos \theta_W} \bar{u}\gamma_\mu \left\{g_L\frac 1 2(1-\gamma_5)+g_{R}\...
ric.san's user avatar
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Charged fermions have both chiralities, with the same mass. Shouldn’t neutrinos, also massive, have both chiralities, though with different masses?

Thanks to answers a previous question, I have realised the difference between helicity, a non-Lorentz-invariant quantity, and the Lorentz invariant chirality. Let me summarise what I understand, ...
Alfred's user avatar
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A thought experiment about neutrinos

I don't understand all the details of Dirac mass, Majorana mass, and many other "deep" notions. I have in mind a very simple thought experiment. Because of neutrino oscillations we know ...
Alfred's user avatar
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How charge conjugation operator flips chirality

I am trying to understand the charge conjugation operator by reading several references online. Until I come to a point which mention that using the anticommutation properties of the Dirac-$\gamma$ ...
Den Jaka's user avatar
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How does an axial vector field transform under a diffeomorphism?

Does it behave like a normal vector field?
ututu's user avatar
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Neutrino field is left-handed

Why if we take the mass of neutrino to be zero then we get only left-handed field when $\psi_r=\frac{1}{2}(1+\gamma^5)\psi$ and $\psi_l=\frac{1}{2}(1-\gamma^5)\psi$ has no dependence on mass?
user avatar
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Coefficient of effective chiral Lagrangian of $\pi\pi$ scattering

I have been suffering from the coefficient in the expansion of chiral lagrangian. Consider $$L=\frac{F^{2}}{4} \rm{Tr}(\partial_{\mu}U^{\dagger}\partial^{\mu}U),$$ where $$U=\exp(i\frac{\phi}{F}).$$ ...
Joe Di.'s user avatar
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How do massless particles have the same chirality and helicity when they are different properties?

I read this article about chirality and helicity. At some point it says For massless particles, chirality is the same as helicity. But as far as I know, helicity takes form in numbers, $(-1/2, +1/2)...
Jungwoon Song's user avatar

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