SQUARE45

The Schwinger action

S_{\text{Schwinger}}

describes the dynamics of the gluon field

A_{\mu}

in the context of effective actions. For a general gauge theory, the action is derived from the path integral over the gauge field

A_{\mu}

S_{\text{Schwinger}}[A] = \int d^4 x \left( \frac{1}{2} (E^a)^2 - \frac{1}{2} (B^a)^2 \right) + \text{gauge fixing terms}

where

E^a

and

B^a

are the electric and magnetic components of the gluon field strength tensor

F^a_{\mu\nu}

. In the pure Yang-Mills limit, the action is simply the Yang-Mills action,

\mathcal{L}_{YM} = -\frac{1}{4} \text{Tr}(F_{\mu\nu} F^{\mu\nu})

Schwinger Action