Functional determinants on certain domains

Functional determinants on various domains of the sphere and flat space are presented for scalar and spinor fields.Comment: 14p, plain TeX, talk presented at the 6th Moscow Quantum Gravity Seminar, Moscow, June 12-19, 1995.(Minor errors corrected.

A Comment on Junction and Energy Conditions in Thin Shells

This comment contains a suggestion for a slight modification of Israel's covariant formulation of junction conditions between two spacetimes, placing both sides on equal footing with normals having uniquely defined orientations. The signs of mass energy densities in thin shells at the junction depend not only on the orientations of the normals and it is useful therefore to discuss the sign separately. Calculations gain in clarity by not choosing the orientations in advance. Simple examples illustrate our point and complete previous classifications of spherical thin shells in spherically symmetric spacetimes relevant to cosmology.Comment: (Tex file + PS file with a figure) Tex errors were correcte

Is the Regge Calculus a consistent approximation to General Relativity?

We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete equations when evaluated on solutions of the Einstein equations. We will show that for generic simplicial lattices the residual errors can not be used to distinguish metrics which are solutions of Einstein's equations from those that are not. We will conclude that either the Regge calculus is an inconsistent approximation to General Relativity or that it is incorrect to use residual errors in the discrete equations as a criteria to judge the discrete equations.Comment: 27 pages, plain TeX, very belated update to match journal articl

O(d,d) invariance at two and three loops

We show that in a two-dimensional sigma-model whose fields only depend on one target space co-ordinate, the O(d,d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion).Comment: 21 pages. Plain Tex. Uses Harvmac ("b" option). Revised Version with references added and minor errors correcte