THE FUNCTIONAL INTEGRAL FOR FIELDS IN A CAVITY

The functional integral for a scalar field confined in a cavity and su bjected to linear boundary conditions is discussed herein. It is shown how the functional measure can be conveniently dealt with by modifyin g the classical action with boundary corrections. The nonuniqueness of the boundary actions is described with a three-parameter family of th em giving identical boundary conditions. In some cases, the correspond ing Green's function will define a kind of generalized Gaussian measur e on function space. The vacuum energy is discussed, paying due attent ion to its anomalous scale dependence, and the physical issues involve d are considered.