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Results tagged with chirality
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user 66086
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.
3
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Explaining "Left" and "Right" to an Alien using Chirality and Helicity
Chirality is also odd under parity (L is sent to R). …
- 66.3k
1
vote
Accepted
Conservation of chirality in non-weak elementary particle interactions
\overline {\psi _L} ~\gamma^\mu \psi_L +eA_\mu \overline {\psi_R} ~\gamma^\mu \psi_R
,
$$
so in the t-channel (exchange) an electron or positron emitting or absorbing a virtual photon preserves its chirality … So at right angle emission, you've lost memory of the original helicities, and basically also chiralities, since helicity and chirality are mismatched by m/p.) …
- 66.3k
2
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Why is the chiral symmetry only $SU(3) \times SU(3)$ and not $SU(6)$?
On second thought, the reason the Noether currents and charges of all such continuous transformations vanish, as per my comments to your answer, @JeffDrorr, is that the transformation $\delta \psi_L = …
- 66.3k
1
vote
Accepted
Is there a relationship between axial $U(1)$ symmetry and parity transformations?
They are both manifestly true. Any confusion is traceable to notational overkill.
In your 2d Weyl basis where superfluous spinor indices are ignored, an axial rotation is but
$$
e^{-i\beta \sigma_3} = …
- 66.3k
0
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Fierz identity with Weyl spinors
There is a straightforward way to get this essentially by inspection, reading off the V×V row of the general Fierz table, (the worked example with an overall minus sign for the anticommuting fermions …
- 66.3k
1
vote
Accepted
Sufficient and Necessary Conditions for Chiral Symmetry Breaking
Yes, you understand correctly,
$$ F_0\neq 0 \qquad \color{red}\Leftrightarrow \qquad\chi SB \tag{↯} \\
\langle \bar qq\rangle\neq 0 \qquad\color{red}\Rightarrow \qquad\chi SB . $$
In the latter case, …
- 66.3k
2
votes
Accepted
Are right-handed chiral particles more stable than left-handed?
Indeed, narrowly speaking, right-chiral muons are stable as they don't decay through the charged weak current (the $W^-$ you mention). The electrons left-chiral muons decay to are also left chiral, a …
- 66.3k
4
votes
Weyl transformation of Dirac equation
Your second equation still is the Dirac equation in the chiral (Weyl) basis of the gamma matrices, which uniformizes $\gamma^0$ with
$\gamma^k$, and is diagonal in chirality, $\gamma^5$,
$$\gamma^0 = …
- 66.3k
1
vote
Explicit Symmetry Breaking in Chiral Lagrangian
This is a storm in a teacup. It is fueled by the conflation of two traces, which the experienced consider as self-explanatory, but confuses the novices.
The exponent on your axial rotation on fermions …
- 66.3k
0
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Shouldn't there be a Particle for Changing Left-handed to Right-handed Particles and Vice Ve...
I gather you appreciate the crucial difference between chirality & helicity for massive particles, and never use L and R for helicity, which is $\pm$. … chiral projectors slip past the $\gamma^0$ implicit in the overbar and flip to the other kind, enforcing the opposite chirality of the particle destroyed by the term. …
- 66.3k
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Particle Physics: Decomposition of a Helicity Spinor
different) left-chiral projection; which is why negative helicity is improperly/confusingly sometimes called "left", and positive helicity is misidentified as "right", to remind you of its connection to chirality …
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2
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Accepted
Calculation of vaccuum expectation value in Chiral Perturbation Theory
As I indicated, I don't wish to make faces at your review article, but the text by TP Chang & LF Li , Ch 5.4, 5.5, is less unfriendly.
In any case, you appear lost, and a trail map of the lay of the …
- 66.3k
2
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Accepted
Distinguishing between left-handed and right-handed weak coupling from electron-neutrino sca...
In real life, the SM, the situation is as follows:
For starters, I flip the definition of the axial coupling w.r.t. yours, so
$$g_V \bar{\psi} \not Z \psi - g_A \bar{\psi} \not Z \gamma^5 \psi,$$ …
- 66.3k
2
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Accepted
Group structure of QCD‘s chiral symmetry (breaking)
You are strictly asking about names used--except I cannot comment on $SU(3)_A$ because there is no such group. I'll skip U(1) because it commutes with all else and is irrelevant for our purposes.
You …
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Accepted
EW theory vertices
Further note L is in no way privileged over R: it is simply a convention of us mooring chirality on leptons/quarks instead of antileptons/antiquarks. …
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