The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect

Understand

One of the most efficient methods for the evaluation of the vacuum expectation values for physical observables in the Casimir effect is based on using the Abel-Plana summation formula.

• This enables to derive the renormalized quantities in a manifestly cutoff independent way and to present them in the form of strongly convergent integrals.
• However, applications of the Abel-Plana formula, in its usual form, are restricted by simple geometries when the eigenmodes have a simple dependence on quantum numbers.
• The author generalized the Abel-Plana formula which essentially enlarges its application range.