chapter  16
6 Pages

Feynman Rules for Vector Fields

As before, the quantisation for vector fields starts by expanding the field in plane waves and identifying the Fourier coefficients with creation and annihilation operators:

Aµ(x) = ∫

d3 k√ 2k0(k)(2π )3

∑ λ

( aλ(k)ε(λ)µ (k)e−ikx + a †λ(k)ε(λ)µ (k)∗eikx

) , (16.1)

where ε(λ)µ (k)e−ikx are independent plane wave solutions of the equations of motion. The index λ enumerates the various solutions for fixed momentum. They will be identified with the spin components or helicity eigenstates of the vector.