The functional integral for fields in a cavity

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Abstract
The functional integral for a scalar field confined in a cavity and subjected to linear boundary conditions is discussed herein. It is shown how the functional measure can be conveniently dealt with by modifying the classical action with boundary corrections. The nonuniqueness of the boundary actions is described with a three-parameter family of them giving identical boundary conditions. In some cases, the corresponding Green’s function will define a kind of generalized Gaussian measure on function space. The vacuum energy is discussed, paying due attention to its anomalous scale dependence, and the physical issues involved are considered.