Vacuum Polarization in a Zero-Range Potential Field

Abstract

The effects of vacuum polarization for a massless scalar field φ(x) in the vicinity of a pointlike source that has a zero-range potential are analyzed in four-dimensional Minkowski space. An exact expression for the regularized scalar-field Hadamard function is obtained by means of the technique of self-adjoint extensions, and the renormalized vacuum expectation values of the scalar field squared, ⟨φ² (x)⟩_ren, and of the operator of the scalar-field energy—momentum tensor, ⟨T_μν(x)⟩_ren, are calculated.