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Questions tagged [chirality]

Chirality is defined through the ±1 eigenvalue under action of γ<sup>5</sup> on ψ, a Dirac field thus projected into its left- or right-handed component by the projection operators (1−γ<sup>5</sup>)/2 or (1+γ<sup>5</sup>)/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 instead of the [helicity] tag: the projectors *must* be implied.

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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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Direction of chiral symmetry breaking

What happens if one breaks the SU(2) chiral symmetry in a non-real direction(a direction apart from the one that the small masses of hadron's constituents(quarks) dictate). Or equivalently We know ...
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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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Vector-like Representation of fermions

In the literature, they often extend the Standard Model by adding a so-called vector-like fermion which is a multiplet invariant under $SU(2)_L\times U(1)$. The left- and right-handed components of ...
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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 ...
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In electromagnetism, why does nature prefer the right-hand rule over the left-hand rule? [duplicate]

At school I learnt the Right-hand rule to remember the resulting direction of different phenomena, such as geometrical cross products, mechanical torque, or the direction a screw will move when ...
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Group structure of QCD‘s chiral symmetry (breaking)

With $3$ flavors of massless quarks, the QCD Lagrangian is invariant under flavor transformations$$SU(3)_V\ \otimes\ SU(3)_A\ \otimes\ U(1)_V\ \otimes\ U(1)_A.$$ Now, this is equivalent to $$SU(3)_R\ \...
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Is there a standard convention for whether the term “handedness” refers to helicity or chirality?

I was under the impression that the "handedness" of a massive spin-1/2 particle refers to its chirality rather than its helicity. This answer, this one and Srednicki's QFT textbook seem to use the ...
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Chirality of the Electromagnetic Field Tensor

I have learned that chirality is a concept, that appears for $(A,B)$ representations of the Lorentz group, where $A\neq B$. An example would be a Dirac spinor, corresponding to the representation $(\...
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Why Majorana neutrinos is a solution for the existence of only LH neutrinos?

At lesson my teacher stated that the possible reason for why only LH neutrinos are observed are that either: neutrinos are Dirac fermion but the RH neutrinos are not interacting weakly or that they ...
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What is the physical interpretation of chirality / chiral anomaly?

I'm dealing with this paper from C. Bär and A. Strohmeier about a rigorous derivation of the chiral anomaly. I'm not quite familiar with the physical context of chirality and its anomaly. What ...
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Are anomalies always undesirable?

In the glossary of the AMS book on Quantum Fields and Strings it is stated that An anomalous theory does not make sense quantum mechanically, so anomaly cancellation is a fundamental requirement ...
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Why do the right-handed up quark and down quark not form an $SU(2)$ doublet?

The left-handed up quark and down quark are an $SU(2)$ doublet $(u, d)_{L}$. Why do their right-handed counterparts, right-handed up quark and down quark, not form an $SU(2)$ doublet $(u, d)_{R}$?
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Is the right-handed electron really an $SU(2)$ singlet?

In the Standard Model, neutrinos are assumed to be massless, and the right-handed neutrinos thus do not exit. Is this the reason that the right-handed electron is regarded as an $SU(2)$ singlet? ...
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Chirality confusion in solutions of Dirac's equation for spin 1/2 particles with mass

Suppose one starts with Dirac's equation for a spin 1/2 particle but without interactions - a free particle with mass. The solutions obtained using a chiral basis of gamma matrices result in left-...
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Block diagonalizing a Hamiltonian using a symmetry

I have the following Hamiltonian, describing the 3 state Chiral clock model in 1D: $$H = -f \sum_{j=1}^L (\tau_j^\dagger e^{-i \phi}+h.c.)-J\sum_{j=1}^{L-1}(\sigma_j^\dagger\sigma_{j+1}e^{-i\hat{\phi}}...
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Time evolution of a massive fermion produced in a state of definite chirality

But for massive particles like an electron, the chirality is not conserved in time i.e. if an electron is produced in the state $e_L$ at time t=0, at a later time it becomes a mixture of left-handed ...
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Why are antiparticles associated with spin-flipped spinors?

In section 2.2 of Elvang and Huang's Scattering Amplitudes in Gauge Theory and Gravity (http://arXiv.org/abs/1308.1697), beneath equation (2.9), it is mentioned that $u^{\pm}=v^{\mp}$, where $u^\pm$ ...
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Why doesn't optical rotation dispersion spectrally overlap with circular dichroism?

From my understanding of Kramer's Kronig relations applied to chirality: optical rotation dispersion should be correlated to circular dichroism. Why is it then that many molecules have an optical ...
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How is chirality defined for row vectors?

When working with Dirac spinors, the chirality of a spinor field is determined by its $\gamma_5$ eigenvalue, so if $\psi_L$ is left-handed then $$\gamma_5 \psi_L = - \psi_L.$$ Some sources define a ...
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Different chirality in IIB (N=2, D=10) supergravity

In some papers on type IIB supergravity (N=2, D=10) the dilatino is taken to be of positive chirality. In some other papers dilatino is choosen instead of negative chirality. Is it possible to map ...
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Weyl transformation of Dirac equation

The Dirac Equation is given by $$\left(i\gamma^\mu\partial_\mu- \frac{mc}{\hbar}\right)\Psi_D = 0,$$ where $\gamma^\mu$ are the Dirac $\gamma$-matrices and $\Psi_D$ is a Dirac spinor. I would like to ...
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Mass of a Dirac neutrino

(I have restated the question after the comments to make it clearer) Is there any way mathematically a Dirac neutrino can have different mass for LH and RH state? The dirac mass term (obtained after ...
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Can neutrinos change chirality?

Since neutrinos interact with the Higgs field, that means it can lose weak hypercharge to the Higgs field and thus flip chirality? (LH: $T_3 = +\frac{1}{2}, Y_w = -1$ RH: $T_3 = 0, Y_w = 0$) (Or, it ...
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Wilson loops, confinement and chiral symmetry relations

As per my limited understanding of confinement, I understood it as phenomenon between fermions of a gauge theory, such as $SU(3)$ gauge theory in the low energy limit (where the coupling constant ...
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What are the differences between chiral states and helical states in condensed matter physics?

As we know in particle physics, chirality corresponds to eigenvalues of the fifth gamma matrix, and helicity corresponds to the value of the projection of spin onto momentum. So in condensed matter ...
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Possible typo in Schwartz's QFT, p. 629

I'm trying to see whether this is my own misunderstanding or a typo in Schwartz's QFT book. Any help or feedback appreciated. Schwartz talks about Chiral anomalies from the integral measure. The ...
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Aliens from antimatter region

If we established a radio contact with an extraterrestrial civilization, assuming the signal latency permits, what question would we ask them to know if they are made of matter or anti-matter? I ...
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Chirality vs Handedness

It seems to me that the terms attributing a particle left- or right-chiral and left- or right-handed are used pretty much interchangeably. Today a colleague argued that strictly speaking ...
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Are all pseudoscalars secretly Goldstone bosons?

A pseudoscalar Goldstone boson, $\pi(x)$, is protected by a shift symmetry: it shows up with a derivative in its interaction terms in a Lagrangian. As a pseudoscalar, we may also write it with the ...
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Is there a relationship between axial $U(1)$ symmetry and parity transformations?

Some books, such as Maggiore, write that the axial $U(1)$ transformation is the chiral transformation. A Dirac field $\Psi \in (\frac12, \frac12)$ undergoes a chiral transformation in the following ...
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Calculation of vaccuum expectation value in Chiral Perturbation Theory

From one point of view I have to admit from the start that this question might be a trivial calculation problem but the truth is, I'm quite stuck. I am studying chiral perturbation theory with the aim ...
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Manifestation of chirality in particle physics

I understand (I hope) the meaning of chirality but I am not really sure how does it affects the weak interaction. From what I understand, an electron is a superposition of left and right chirality ...
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Is there any way to determine the handedness of a molecule through remote spectroscopy?

In following publications of astronomy, one will come across findings of various molecules (sometimes organic) that have been detected spectroscopically. Is there any way to determine the handedness ...
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Chirality in feynman diagrams

In quantum mechanics chirality is preserved for massless particles. But in Standard Model, is there any reason for chirality to be preserved for massless particles in annihilation diagrams? (unless ...
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What's chiral about the Dirac points in graphene?

One of the main interesting properties of graphene is the appearance of Dirac points in its energy band structure, i.e. the presence of points where the valence and conduction bands meet at conical ...
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Quantum Mechanical description of chiral molecule

I am a theoretical physicist by training and I need to consider polarized light interacting quantum mechanically with a single molecule of sugar. I have never done theoretical chemistry and really ...
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Is chirality an intrinsic property of elementary fermions?

Is it the case that chirality is an intrinsic property of elementary fermions? I mean, is it the case that all electrons have left handed chirality while all positrons have right handed chirality? And ...
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Does any unifying theory explain why nature is Chiral?

I'm currently studying particle physics and find the experimental fact that massless particles are always left-handed quite surprising.In fact, the need to add projectors in the lagrangian seems not ...
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Axial symmetry, “left handed and right handed” and “particle and antiparticle”?

In Srednicki's text book the axial symmetry is described as invariance under, $$\Psi (x) \rightarrow e^{-i\alpha (x) \gamma_5}\Psi(x)$$ and $$\bar \Psi (x) \rightarrow \bar \Psi e^{-i\alpha (x) \...