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
( 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.