Editing Propagator (section)

==== Spin 1 ====
The propagator for a [[gauge boson]] in a [[gauge theory]] depends on the choice of convention to fix the gauge. For the gauge used by Feynman and [[Ernst Stueckelberg|Stueckelberg]], the propagator for a [[photon]] is
:<math>{-i g^{\mu\nu} \over p^2 + i\varepsilon }.</math>

The general form with gauge parameter {{math|''λ''}}, up to overall sign and the factor of <math>i</math>, reads
:<math> -i\frac{g^{\mu\nu} + \left(1-\frac{1}{\lambda}\right)\frac{p^\mu p^\nu}{p^2}}{p^2+i\varepsilon}.</math>

The propagator for a massive vector field can be derived from the Stueckelberg Lagrangian. The general form with gauge parameter {{math|''λ''}}, up to overall sign and the factor of <math>i</math>, reads
:<math> \frac{g_{\mu\nu} - \frac{k_\mu k_\nu}{m^2}}{k^2-m^2+i\varepsilon}+\frac{\frac{k_\mu k_\nu}{m^2}}{k^2-\frac{m^2}{\lambda}+i\varepsilon}.</math>

With these general forms one obtains the propagators in unitary gauge for {{math|''λ'' {{=}} 0}}, the propagator in Feynman or 't Hooft gauge for {{math|''λ'' {{=}} 1}} and in Landau or Lorenz gauge for {{math|''λ'' {{=}} ∞}}. There are also other notations where the gauge parameter is the inverse of {{mvar|λ}}, usually denoted {{mvar|ξ}} (see [[Gauge fixing#Rξ gauges|{{math|''R''<sub>ξ</sub>}} gauges]]). The name of the propagator, however, refers to its final form and not necessarily to the value of the gauge parameter.

Unitary gauge:
:<math>\frac{g_{\mu\nu} - \frac{k_\mu k_\nu}{m^2}}{k^2-m^2+i\varepsilon}.</math>

Feynman ('t Hooft) gauge:
:<math>\frac{g_{\mu\nu}}{k^2-m^2+i\varepsilon}.</math>

Landau (Lorenz) gauge:
:<math>\frac{g_{\mu\nu} - \frac{k_\mu k_\nu}{k^2}}{k^2-m^2+i\varepsilon}.</math>