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I'm trying to remind myself of exactly what, physically, is the difference between V and A couplings. Now, a vector coupling is of the form [tex]\bar{\psi}\gamma^\mu\psi[/tex], and axial coupling of the form [tex]\bar{\psi}\gamma^\mu\gamma^5\psi[/tex]. Thinking in terms of a chiral fermion expanded as:

[tex]

f = \left[\left(\frac{1-\gamma^5}{2}\right) + \left(\frac{1+\gamma^5}{2}\right)\right]\psi

[/tex]

and where [tex]\bar{f} = \gamma^\dagger\gamma^0[/tex], I assume the difference between the V and A couplings has to do with how the L and R projection operators commute through either [tex]\gamma^\mu[/tex] or [tex]\gamma^\mu\gamma^5[/tex] from the 'coupling' term, and the [tex]\gamma^0[/tex] from the conjugate field term in a given Lagrangian.

However, as [tex][\gamma^5,\gamma^5] = 0[/tex], I don't see how a difference in the chiral treatment between V and A couplings can arise. Am I barking up completely the wrong tree? Any insight welcomed!

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# Physical interpretation of V and A couplings

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