7,524 research outputs found
Further functional determinants
Functional determinants for the scalar Laplacian on spherical caps and
slices, flat balls, shells and generalised cylinders are evaluated in two,
three and four dimensions using conformal techniques. Both Dirichlet and Robin
boundary conditions are allowed for. Some effects of non-smooth boundaries are
discussed; in particular the 3-hemiball and the 3-hemishell are considered. The
edge and vertex contributions to the coefficient are examined.Comment: 25 p,JyTex,5 figs. on request
Smeared heat-kernel coefficients on the ball and generalized cone
We consider smeared zeta functions and heat-kernel coefficients on the
bounded, generalized cone in arbitrary dimensions. The specific case of a ball
is analysed in detail and used to restrict the form of the heat-kernel
coefficients on smooth manifolds with boundary. Supplemented by conformal
transformation techniques, it is used to provide an effective scheme for the
calculation of the . As an application, the complete coefficient
is given.Comment: 23 pages, JyTe
Effects on QCD in and
The combined LEP and SLD measurements of R b are about three standard deviations above the standard model. The measurement techniques employed are claimed to be highly reliable and systematically safe. R c , which is measured using different and inherently less reliable techniques, is found to be 1.7 standard deviations low. In this paper, I will examine what constraints the measurements of put on these measurements. I will also explore possible sources of systematics related to the models used to account for QCD effects in the processes measured
Interactions of a String Inspired Graviton Field
We continue to explore the possibility that the graviton in two dimensions is
related to a quadratic differential that appears in the anomalous contribution
of the gravitational effective action for chiral fermions. A higher dimensional
analogue of this field might exist as well. We improve the defining action for
this diffeomorphism tensor field and establish a principle for how it interacts
with other fields and with point particles in any dimension. All interactions
are related to the action of the diffeomorphism group. We discuss possible
interpretations of this field.Comment: 12 pages, more readable, references adde
Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region
We suggest a method of construction of general diffeomorphism invariant
boundary conditions for metric fluctuations. The case of dimensional
Euclidean disk is studied in detail. The eigenvalue problem for the Laplace
operator on metric perturbations is reduced to that on -dimensional vector,
tensor and scalar fields. Explicit form of the eigenfunctions of the Laplace
operator is derived. We also study restrictions on boundary conditions which
are imposed by hermiticity of the Laplace operator.Comment: LATeX file, no figures, no special macro
Prolongations of Geometric Overdetermined Systems
We show that a wide class of geometrically defined overdetermined semilinear
partial differential equations may be explicitly prolonged to obtain closed
systems. As a consequence, in the case of linear equations we extract sharp
bounds on the dimension of the solution space.Comment: 22 pages. In the second version, a comparison with the classical
theory of prolongations was added. In this third version more details were
added concerning our construction and especially the use of Kostant's
computation of Lie algebra cohomolog
Heat Kernel Expansion for Semitransparent Boundaries
We study the heat kernel for an operator of Laplace type with a
-function potential concentrated on a closed surface. We derive the
general form of the small asymptotics and calculate explicitly several
first heat kernel coefficients.Comment: 16 page
The heat kernel coefficient for oblique boundary conditions
We present a method for the calculation of the heat kernel
coefficient of the heat operator trace for a partial differential operator of
Laplace type on a compact Riemannian manifold with oblique boundary conditions.
Using special case evaluations, restrictions are put on the general form of the
coefficients, which, supplemented by conformal transformation techniques,
allows the entire smeared coefficient to be determined.Comment: 30 pages, LaTe
Heat-kernel coefficients for oblique boundary conditions
We calculate the heat-kernel coefficients, up to , for a U(1) bundle on
the 4-Ball for boundary conditions which are such that the normal derivative of
the field at the boundary is related to a first-order operator in boundary
derivatives acting on the field. The results are used to place restrictions on
the general forms of the coefficients. In the specific case considered, there
can be a breakdown of ellipticity.Comment: 9 pages, JyTeX. One reference added and minor corrections mad
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