225 research outputs found
Heat-kernels and functional determinants on the generalized cone
We consider zeta functions and heat-kernel expansions on the bounded,
generalized cone in arbitrary dimensions using an improved calculational
technique. The specific case of a global monopole is analysed in detail and
some restrictions thereby placed on the coefficient. The computation
of functional determinants is also addressed. General formulas are given and
known results are incidentally, and rapidly, reproduced.Comment: 26p,LaTeX.(Cosmetic changes and eqns (9.8),(11.2) corrected.
Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
In this article we consider the zeta regularized determinant of Laplace-type
operators on the generalized cone. For {\it arbitrary} self-adjoint extensions
of a matrix of singular ordinary differential operators modelled on the
generalized cone, a closed expression for the determinant is given. The result
involves a determinant of an endomorphism of a finite-dimensional vector space,
the endomorphism encoding the self-adjoint extension chosen. For particular
examples, like the Friedrich's extension, the answer is easily extracted from
the general result. In combination with \cite{BKD}, a closed expression for the
determinant of an arbitrary self-adjoint extension of the full Laplace-type
operator on the generalized cone can be obtained.Comment: 27 pages, 2 figures; to appear in Manuscripta Mathematic
Chiral bag boundary conditions on the ball
Local boundary conditions for spinor fields are expressed in terms of a
1-parameter family of boundary operators, and find applications ranging from
(supersymmetric) quantum cosmology to the bag model in quantum chromodynamics.
The present paper proves that, for massless spinor fields on the Euclidean ball
in dimensions d=2,4,6, the resulting zeta(0) value is independent of such a
theta parameter, while the various heat-kernel coefficients exhibit a
theta-dependence which is eventually expressed in a simple way through
hyperbolic functions and their integer powers.Comment: 30 pages, REVTe
Bose-Einstein condensation for interacting scalar fields in curved spacetime
We consider the model of self-interacting complex scalar fields with a rigid
gauge invariance under an arbitrary gauge group . In order to analyze the
phenomenon of Bose-Einstein condensation finite temperature and the possibility
of a finite background charge is included. Different approaches to derive the
relevant high-temperature behaviour of the theory are presented.Comment: 28 pages, LaTe
Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension
In this paper we compute the coefficients of the heat kernel asymptotic
expansion for Laplace operators acting on scalar functions defined on the so
called spherical suspension (or Riemann cap) subjected to Dirichlet boundary
conditions. By utilizing a contour integral representation of the spectral zeta
function for the Laplacian on the spherical suspension we find its analytic
continuation in the complex plane and its associated meromorphic structure.
Thanks to the well known relation between the zeta function and the heat kernel
obtainable via Mellin transform we compute the coefficients of the asymptotic
expansion in arbitrary dimensions. The particular case of a -dimensional
sphere as the base manifold is studied as well and the first few heat kernel
coefficients are given explicitly.Comment: 26 Pages, 1 Figur
The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type
In this work we study the spectral zeta function associated with the Laplace
operator acting on scalar functions defined on a warped product of manifolds of
the type where is an interval of the real line and is a
compact, -dimensional Riemannian manifold either with or without boundary.
Starting from an integral representation of the spectral zeta function, we find
its analytic continuation by exploiting the WKB asymptotic expansion of the
eigenfunctions of the Laplace operator on for which a detailed analysis is
presented. We apply the obtained results to the explicit computation of the
zeta regularized functional determinant and the coefficients of the heat kernel
asymptotic expansion.Comment: 29 pages, LaTe
Models for Synthetic Aperture Radar Image Analysis
After reviewing some classical statistical hypothesis commonly used in image processing and analysis, this paper presents some models that are useful in synthetic aperture radar (SAR) image analysis
Ab initio Calculations of Multilayer Relaxations of Stepped Cu Surfaces
We present trends in the multilayer relaxations of several vicinals of
Cu(100) and Cu(111) of varying terrace widths and geometry. The electronic
structure calculations are based on density functional theory in the local
density approximation with norm-conserving, non-local pseudopotentials in the
mixed basis representation. While relaxations continue for several layers, the
major effect concentrates near the step and corner atoms. On all surfaces the
step atoms contract inwards, in agreement with experimental findings.
Additionally, the corner atoms move outwards and the atoms in the adjacent
chain undergo large inward relaxation. Correspondingly, the largest contraction
(4%) is in the bond length between the step atom and its bulk nearest neighbor
(BNN), while that between the corner atom and BNN is somewhat enlarged. The
surface atoms also display changes in registry of upto 1.5%. Our results are in
general in good agreement with LEED data including the controversial case of
Cu(511). Subtle differences are found with results obtained from semi-empirical
potentials.Comment: 21 pages and 3 figure
Polymerization activity of an alpha-like DNA polymerase requires a conserved 3'-5' exonuclease active site
Most DNA polymerases are multifunctional proteins that possess both polymerizing and exonucleolytic activities. For Escherichia coli DNA polymerase I and its relatives, polymerase and exonuclease activities reside on distinct, separable domains of the same polypeptide. The catalytic subunits of the a-like DNA polymerase family share regions of sequence homology with the 3'-5 ' exonuclease active site of DNA polymerase I; in certain a-like DNA polymerases, these regions of homology have been shown to be important for exonuclease activity. This finding has led to the hypothesis that a-like DNA polymerases also contain a distinct 3'-5' exonuclease domain. We have introduced conservative substitutions into a 3'-5 ' exonuclease active site homology in the gene encoding herpes simplex virus DNA polymerase, an a-like polymerase. Two mutants were severely impaired for viral DNA replication and polymerase activity. The mutants were not detectably affected in the ability of the polymerase to interact with its accessory protein, UL42, or to colocalize in infected cell nuclei with the major viral DNA-binding protein, ICP8, suggesting that the mutation did not exert global effects on protein folding. The results raise the possibility that there is a fundamental difference between a-like DNA polymerases and E. coli DNA polymerase I, with less distinction between 3'-5 ' exonuclease and polymerase functions in a-like DNA polymerases. DNA polymerases are central to the replication of geneti
A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds
We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the AtiyahâSinger index theorem and another term involving the η -invariant of the Cauchy hypersurfaces
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