Photon

A photon is a quantum of the electromagnetic field with energy $E=h\nu =\hslash \omega$.

For a real on shell photon of null momentum $k$, a physical polarization satisfies $k\cdot ϵ=0$ and is defined modulo $ϵ\mapsto ϵ+\alpha k$. The two-dimensional quotient carries the two physical photon helicities. In a transverse gauge choose ${ϵ}^0=0$ and ${ϵ}^{\ast }\cdot ϵ=-1$. A Ward identity ensures that replacing an external polarization by its momentum gives zero in the summed physical amplitude.

Two first-class constraints in Maxwell theory remove four phase-space variables from the eight variables of a four-component potential and its momenta. The remaining four phase-space variables form two canonical pairs. In radiation gauge these are transverse polarization modes; circular combinations have helicity $+1$ and $-1$. Auxiliary covariant-gauge components do not add physical photon states.

Photon absorption removes a photon and transfers its energy and momentum to matter. It contributes a negative photon-number collision source. It differs from Compton scattering, which redistributes a photon's energy and direction while preserving the count. The integrated source can vanish if photon emission and absorption balance.

Photon emission creates a photon, for example in bremsstrahlung or the decay of an excited material state. It produces a positive photon-number collision source when not balanced by inverse processes. The photon number current is conserved only if its integrated creation and destruction rates cancel.