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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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 ...
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When did spin and chirality first become a property of particles?
How do particles acquire their spin and chirality? Most specifically, what mechanism drove the particles during the BB to acquire their specific spins and chiralities, and at what point in the BB's ...
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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 ...
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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 ...
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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{...
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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 ...
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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 ...
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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, ...
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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))
$$J_W^{\mu+}=\frac{1}{\sqrt{2}}\bar{\nu}_{\mu L}\gamma^{\mu}\mu_L \quad J_W^{\mu-...
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How does the factor $m_b$ arise in the weak effective operator $\mathcal{O}_7^\gamma$?
According to [1] one of the dominant operators contributing to the decay $B \rightarrow K^{(*)} \ell^+ \ell^-$ is given by $\mathcal{O}_7^\gamma$.
When calculating the coefficient of this operator ...
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Lattice version of axial the current in (1+1)-d
I am studying (1+1)-d Driac fermion for a lattice formulation.
The spinor $\psi$ has two components (the upper $\psi_1$ and lower $\psi_2$ components, $\psi = (\psi_1,\psi_2)^T$ )
and in the ...
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Chiral transformation of lattice fermionic operators
Consider the Hamiltonian of interacting particles on a lattice, e.g. the Hubbard Hamiltonian
$$
H = -t \sum_{i\sigma} ( c_{i,\sigma}^{\dagger} c_{i+1,\sigma} + \mathrm{h.c.} ) + U\sum_i n_{i\uparrow} ...
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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.
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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?
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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....
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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 ...
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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}\...
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How is the formula for specific rotation derived?
I wanted to find the complete derivation for specific rotation in chiral compounds. Where would that be available or does anyone know the derivation themselves and could share? I would want a formula ...
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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, ...
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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 ...
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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$ ...
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How does an axial vector field transform under a diffeomorphism?
Does it behave like a normal vector field?
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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?
user321957
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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}).$$ ...
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Chiral Transformation and Dirac Bilinear
I need to compute the following Dirac bilinears:
$$\overline{\psi} \psi \quad \text{and} \quad \overline{\psi} \gamma_\mu \psi$$
Under the following Chiral transformation:
$$\psi \rightarrow \psi' = \...
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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)...
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Chiral symmetry of the Dirac Lagrangian
I need to show that in the mass to zero limit the lagrangian density:
$$\mathcal{L}=\bar{\psi}(i\gamma^\mu\partial_\mu-m)\psi$$
is invariant under the transformations:
$$\psi'=e^{i\alpha\gamma^5} \psi$...
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If the universe was dominated by antimatter instead of matter, would we physically notice?
I read that antimatter and matter are identical aside from their opposite charge and quantum number. Of course, the mystery of why matter dominates in our universe is an active field of research. But ...
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Two different types of circularly polarized light
Circularly polarized light [$\mathbf{E}=E_0e^{-i\omega t}(\hat{x}+i\hat{y})$] usually refers to the light whose propagation direction is perpendicular to the polarization plane, like this figure on ...
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Why does "chiral symmetry" in the Altland-Zirnbauer classification mean something different to other contexts?
The Altland-Zirnbauer classification of random matrices is based on three symmetries: time-reversal, charge conjugation, and a third which is sometimes referred to as "chiral" or "...
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Why do we use "vector-like" to mean "non-chiral", in particle physics?
I've been reading some stuff about searches for vector-like quarks and vector-like leptons, and I'm a little confused about the terminology.
Also, I'm a little new to this, so bear with me.
As far as ...
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Working through the solution of the Ozma problem
I’m trying to work through the Ozma problem and the Wu experiment to get a better handle on parity and I’m being tripped up by something which is almost certainly trivial.
I can explain negative ...
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Transformation of Chern-Simons type action under large $SO(4)$ gauge transformation
For the Chern-Simons action
$$S = \kappa \epsilon^{\mu\nu\delta}tr(A_\mu\partial_\nu A_\delta + \frac{2}{3}A_\mu A_\nu A_\delta)$$
under a large gauge transformation
$$A_\mu \rightarrow g^{-1}A_\mu g +...
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Are there in nature any Right Chiral isolated electron particles?
Note: I refrain from using the concept of handedness and the terms left-handed and right-handed when referring to chirality since these usually refer to the helicity of charged fermions and their ...
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What is spectral flow of electrons?
While reading about chiral anomaly in condensed matter systems, I came across the term electron Spectral flow. I have no idea what this is and where to look for understanding this. Please help.
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The relation of gamma matrix between field operator change and chirality in Peskin and Schroeder (page 165)
I'm reading Compton scattering in Peskin's book (page 165) and there is a sentence I can't understand.
The third sentence in the above paragraph says that three $\gamma$-matrix between field operator ...
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Charge term in the chiral Lagrangian with dynamical photons
When constructing the effective Lagrangian, we parametrize the Goldstone bosons (such as the pions $\pi_a$) by $U = \exp(i \pi_a \tau_a/2 f)$, where $\tau_a$ are the Pauli matrices. (See e.g. here). ...
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Chirality vs Helicity in Top Quark Decay
I still have not had a good explanation of how a Right Handed Top Quark decays.
As I understand it, helicity and chirality are both a part of spin. Does this mean that if either is left handed, the ...
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Are the definitions of chirality in continuum QFT and the Nielsen-Ninomiya theorem equivalent?
I have seen two definitions of chirality in quantum field theory:
According to the Wikipedia article, chirality is defined as whether a particle transforms under a left- or right-handed ...
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Are there chiral fermions in $d=4$ Euclidean space?
In $d=4$ Euclidean space the spin group is $\operatorname{Spin}(4)\cong SU(2)\times SU(2)$ where the two $SU(2)$’s are independent (as opposed to Lorentzian signature where they conjugate into each ...
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Right-handed neutrinos Lagrangian and drawing Feynman diagrams from it
The Lagrangian for the right handed neutrino field is:
$$
L_{\nu} = y_{\alpha i} \bar{L_{\alpha}} H^{\dagger} N_{i} + m_{i} \bar{N^{c}_{i}N_{i}}
$$
With $ L_{\alpha} $ being the left-handed lepton ...
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Where are the right-handed leptons?
So the weak force only works on left-handed leptons and quarks. Does this mean there are no right-handed leptons and quarks?
If there are, why don't we see an abundance of right-handed particles that ...
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Lagrangian density transformation
In a calculation of a Lagrangian density $$
\mathcal{L}=\bar{\psi}\left(i \gamma^{\mu} \partial_{\mu}-m+i \gamma_{5} m^{\prime}\right) \psi.
$$
In order to see if it is invariant or not with the ...
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Handedness over the current terms in Feynman diagrams
This is a question about the Feynman diagrams: imagine I want to calculate the following process:
$$\nu_{e, L} + e^-_R \rightarrow \nu_{e, L} + e^-_R$$
I can have a t-channel diagram with $e^-_R e^-...
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Fermi's theory and left-handed anti-neutrino
I calculated the $\mu \rightarrow e^- + \nu_{\mu} + \bar{\nu}_{e}$ both in Fermi's theory (V-A) and Intermediate Vector Boson theory and IVB at first order seems to match with Fermi's theory which is ...
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How to show that $\bar{\psi}\gamma^{\mu}\psi$ goes to 0 if $\psi$ is are not both left/right handed?
How do you show, using the Dirac matrices, that the above expression is $0$? I have tried substituting $\psi^{\dagger}\gamma^{0}$ in for $\bar{\psi}$ but I cannot find any identities linking $\gamma^{...
user319271
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How do we show that for massless fermions, Helcity and Chirality align?
The Helicity operator of a representation of the Lorentz group is given by $$h = \varepsilon_{ijk}S^{jk}\frac{P^i}{|P|}$$ where $S^{\mu\nu}$ are the generators of the Lorentz group.
In the $(\frac{1}{...
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What are the real Electromagnetic fields of Circularly Polarized Light?
It is my understanding that the $\vec{E}$ and $\vec{B}$ fields of a circularly polarized photon sit purely in the $(1,0)$ or $(0,1)$ representation of the (complexified) Lorentz Group, and have ...
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