Question

Why is the axial current said to create particles?

Answer 1

In Peskin and Schroeder p. 669 it is argued that the axial current can be parametrized between the vacuum and an on-shell pion state as:

<0|

j

μ5

(x)|

π

b

(p)>=−i

p

μ

f

π

δ

ab

e

−ipx

<0|jμ5(x)|πb(p)>=−ipμfπδabe−ipx

This is then described as a parametrization of the amplitude for the axial current to create a pion state from the vacuum. This interpretation puzzles me: isn't it the role of the creation operators of a given theory to do this? Does the above expression correspond to an actual physical process or is it just part of an amplitude in a Feynman diagram for an actual process?

Answer 2

In Peskin and Schroeder p. 669 it is argued that the axial current can be parametrized between the vacuum and an on-shell pion state as: $$<0|j^{\mu 5}(x)|\pi^b(p)>=-ip^\mu f_\pi$$