Digestible Quantum Field Theory by Andrei Smilga

Author:Andrei Smilga
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(11.4)

[see also the footnote after (9.​36)].

Let now replace the electron field by the quark field carrying the colour index, . It is clear that the mass term in (11.1), replaced by , is now invariant under local non-Abelian SU(3) transformations,

(11.5)

with .

We now go over to the first term in (11.1). It is clear again that the free fermion kinetic term is easily generalized to . This structure is not invariant, however, with respect to local gauge transformations (11.5); it is only invariant under global SU(3) transformations where is one and the same at all space-time points.

To write the interaction term, we replace (11.2) by1

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