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indigojoker
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Is there a difference between [tex] (1-\gamma^5) [/tex] and [tex] (1-\gamma_5) [/tex] ? I see the two used interchangeably when calculating cross section.
You will not be able to find all answers to all questions in books. Try to do the calculation by yourself as indicated earlier, it is much more rewarding.indigojoker said:Well, Perkins 3rd edition page 383 gives the amplitude using [tex]\gamma_5[/tex] while Halzen and Martin calculates the amplitude using [tex]\gamma^5[/tex] on equation 12.56
I'm not sure why they could be interchanged.
indigojoker said:Is there a difference between [tex] (1-\gamma^5) [/tex] and [tex] (1-\gamma_5) [/tex] ? I see the two used interchangeably when calculating cross section.
nrqed said:An important point is that one may write gamma_5 as
[tex] \gamma_5 = \frac{i}{4!} ~\epsilon_{\mu \nu \rho \sigma} \gamma^\mu \gamma^\nu \gamma^\rho \gamma^\sigma [/tex]
The difference between (1-\gamma^5) and (1-\gamma_5) lies in their mathematical representations. (1-\gamma^5) represents the projection operator for left-handed particles, while (1-\gamma_5) represents the projection operator for right-handed particles.
No, (1-\gamma^5) and (1-\gamma_5) cannot be used interchangeably. They have different mathematical representations and therefore have different physical meanings.
(1-\gamma^5) and (1-\gamma_5) are used in cross section calculations to account for the spin of particles. (1-\gamma^5) accounts for the spin of left-handed particles, while (1-\gamma_5) accounts for the spin of right-handed particles.
Yes, in certain cases where the particles involved have equal left- and right-handed components, (1-\gamma^5) and (1-\gamma_5) may give the same result. However, this is not always the case and it is important to use the correct operator for the specific particles involved.
(1-\gamma^5) and (1-\gamma_5) are related to parity in particle physics because they represent the projection operators for left- and right-handed particles, respectively. Parity is a fundamental symmetry in particle physics that describes the behavior of particles under spatial inversion, and these operators play a role in this symmetry.