Neumann Casimir effect: A singular boundary-interaction approach

C.D. FOSCO, F.C. LOMBARDO B, F.D. MAZZITELLI

PHYSICS LETTERS B

ELSEVIER SCIENCE BV

Lugar: Amsterdam; 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 quadraticallyto 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 transmissioncoefficients ill-defined because of UV divergences. We present a possible procedure to tame thosedivergences, by introducing a minimum length scale, related to the nonzero ‘width’ of a nonlocal term. Wethen use this setup to reach (either exact or imperfect) Neumann conditions, by taking the appropriatelimits. After defining meaningful reflection coefficients, we calculate the Casimir energies for flat parallelmirrors, presenting also the extension of the procedure to the case of arbitrary surfaces. Finally, wediscuss briefly how to generalize the worldline approach to the nonlocal case, what is potentially usefulin order to compute Casimir energies in theories containing nonlocal potentials; in particular, those whichwe use to reproduce Neumann boundary conditions.