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, ⟨Tμν(x)⟩ren, are calculated.
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