Neumann Casimir effect: a singular boundary-interaction approach

C. D. FOSCO F. C. LOMBARDO F. D. MAZZITELLI

PHYSICS LETTERS B

ELSEVIER SCIENCE BV

Año: 2010 vol. 690 p. 189 - 195

0370-2693

Dirichlet boundary conditions on a surface can be imposed on a scalar field, by coupling it quadratically to a δ-like potential, the strength of which tends to infinity. Neumann conditions, on the other hand, require the introduction of an even more singular term, which renders the reflection and transmission coefficients ill-defined because of UV divergences. We present a possible procedure to tame  those divergences, by introducing a minimum length scale, related to the non-zero ‘width’ of a  nonlocal term. We then use this setup to reach (either exact or imperfect) Neumann conditions, by taking the appropriate limits. After defining meaningful reflection coefficients, we calculate the Casimir energies for flat parallel mirrors, presenting also the extension of the procedure to the case of arbitrary surfaces. Finally, we discuss briefly how to generalize the worldline approach to the nonlocal case, what is potentially useful in order to compute Casimir energies in theories containing nonlocal potentials; in particular, those which we use to reproduce Neumann boundary conditions.