There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.
Abstract
Whenever real particle production occurs in quantum field theory, the imaginary part
of the Hadamard Elementary function \(G^{(1)}\) is non-vanishing. A method is presented
whereby the imaginary part of \(G^{(1)}\) may be calculated for a charged scalar field
in a static spherically symmetric spacetime with arbitrary curvature coupling and
a classical electromagnetic field \(A^{\mu}\). The calculations are performed in Euclidean
space where the Hadamard Elementary function and the Euclidean Green function are
related by \((1/2)G^{(1)}=G_{E}\). This method uses a \(4^{th}\) order WKB approximation
for the Euclideanized mode functions for the quantum field. The mode sums and integrals
that appear in the vacuum expectation values may be evaluated analytically by taking
the large mass limit of the quantum field. This results in an asymptotic expansion
for \(G^{(1)}\) in inverse powers of the mass \(m\) of the quantum field. Renormalization
is achieved by subtracting off the terms in the expansion proportional to nonnegative
powers of \(m\), leaving a finite remainder known as the ``DeWitt-Schwinger approximation.''
The DeWitt-Schwinger approximation for \(G^{(1)}\) presented here has terms proportional
to both \(m^{-1}\) and \(m^{-2}\). The term proportional to \(m^{-2}\) will be shown to
be identical to the expression obtained from the \(m^{-2}\) term in the generalized
DeWitt-Schwinger point-splitting expansion for \(G^{(1)}\). The new information obtained
with the present method is the DeWitt-Schwinger approximation for the imaginary part
of \(G^{(1)}\), which is proportional to \(m^{-1}\) in the DeWitt-Schwinger approximation
for \(G^{(1)}\) derived in this paper.