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confined to a D-dimensional cube Ariel Edery McGill Using a direct sum approach, I calculate as a function of the spatial dimension D the Casimir Energy for the longitudinal (acoustic) modes of a Relativistic Perfect Fluid confined to a D-dimensional cube. The technique I used/developed to do this calculation involves a repeated use of the Euler-Maclaurin integration formula: a formula relating the sum of a function to its integral + some extra terms. One result is that the Casimir Energy is negative for all D in contrast to the case of a D-dimensional sphere. I will begin by illustrating the use of the Euler-Maclaurin integration formula for a simple one-dimensional object: the Casimir Energy of the open Bosonic String.
Tuesday, June 20th 2000, 13:00 |