Divergence terms in the supertrace heat asymptotics for the de Rham complex on a manifold with boundary

We use invariance theory to determine the coefficient $a_{m+1,m}^{d+\delta}$ in the supertrace for the twisted de Rham complex with absolute boundary conditions.Comment: 19 pages, LaTeX, Theorem 1.2 correcte

Geometric realizations of generalized algebraic curvature operators

We study the 8 natural GL equivariant geometric realization questions for the space of generalized algebraic curvature tensors. All but one of them is solvable; a non-zero projectively flat Ricci antisymmetric generalized algebraic curvature is not geometrically realizable by a projectively flat Ricci antisymmetric torsion free connection

Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series

Let G be a compact Lie group acting transitively on Riemannian manifolds M and N. Let p be a G equivariant Riemannian submersion from M to N. We show that a smooth differential form on N has finite Fourier series if and only if the pull back has finite Fourier series on

Nilpotent noncommutativity and renormalization

We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new 4-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizablility properties of NC theories.Comment: 5 figures, a reference adde

Euclidean Scalar Green Function in a Higher Dimensional Global Spacetime

We construct the explicit Euclidean scalar Green function associated with a massless field in a higher dimensional global monopole spacetime, i.e., a $(1+d)$-spacetime with $d\geq3$ which presents a solid angle deficit. Our result is expressed in terms of a infinite sum of products of Legendre functions with Gegenbauer polynomials. Although this Green function cannot be expressed in a closed form, for the specific case where the solid angle deficit is very small, it is possible to develop the sum and obtain the Green function in a more workable expression. Having this expression it is possible to calculate the vacuum expectation value of some relevant operators. As an application of this formalism, we calculate the renormalized vacuum expectation value of the square of the scalar field, $_{Ren.}$, and the energy-momentum tensor, $_{Ren.}$, for the global monopole spacetime with spatial dimensions $d=4$ and $d=5$.Comment: 18 pages, LaTex format, no figure

Antisymmetric tensor fields on spheres: functional determinants and non--local counterterms

The Hodge--de Rham Laplacian on spheres acting on antisymmetric tensor fields is considered. Explicit expressions for the spectrum are derived in a quite direct way, confirming previous results. Associated functional determinants and the heat kernel expansion are evaluated. Using this method, new non--local counterterms in the quantum effective action are obtained, which can be expressed in terms of Betti numbers.Comment: LaTeX, 22 pages, no figure

On the geometric boundaries of hyperbolic 4-manifolds

We provide, for hyperbolic and flat 3-manifolds, obstructions to bounding hyperbolic 4-manifolds, thus resolving in the negative a question of Farrell and Zdravkovska.Comment: 8 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper5.abs.htm