The trace identity and the planar Casimir effect

Abstract

The familiar trace identity associated with the scale transformation xxxx on the Lagrangian density for a noninteracting massive real scalar field in 2 + 1 dimensions is shown to be violated on a single plate on which the Dirichlet boundary condition xxxx is imposed.It is however respected in : i. 1 + 1 dimensions in both free space and on a single plate on which the Dirichlet boundary condition xxxx holds; and, ii. in 2 + 1 dimensions in free space, i.e. the unconstrained configuration.On the plate where xxxx, the modified trace identity is shown to be anomalous with a numerical coefficient for the anomalous term equal to the canonical scale dimension viz.1/2. The technique of Bordag,Robaschik and Wieczorek [5] is used to incorporate the said boundary condition into the generating functional for the connected Green's functions. Note: The xxxx in the abstract above refer to symbols that are available in the abstract of the paper.