Related papers: New Results in Heat-Kernel Asymptotics on Manifold…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
The formulation of gauge theories on compact Riemannian manifolds with boundary leads to partial differential operators with Gilkey--Smith boundary conditions, whose peculiar property is the occurrence of both normal and tangential…
The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…
The covariant technique for calculating the heat kernel asymptotic expansion for an elliptic differential second order operator is generalized to manifolds with boundary. The first boundary coefficients of the asymptotic expansion which are…
I give a short guide into applications of the heat kernel technique to string/brane physics with an emphasis on the emerging boundary value problems.
The boundary-value problem for Laplace-type operators acting on smooth sections of a vector bundle over a compact Riemannian manifold with generalized local boundary conditions including both normal and tangential derivatives is studied.…
We calculate the heat-kernel coefficients, up to $a_2$, 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…
We study the spectral geometry of an operator of Laplace type on a manifold with a singular surface. We calculate several first coefficients of the heat kernel expansion. These coefficients are responsible for divergences and conformal…
The high temperature asymptotics of the Helmholtz free energy of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…
We obtain pointwise lower bounds for heat kernels of higher order differential operators with Dirichlet boundary conditions on bounded domains in $\R^N$. The bounds exhibit explicitly the nature of the spatial decay of the heat kernel close…
The quantisation of gauge theories usually procedes through the introduction of ghost fields and BRST symmetry. In the case of quantum gravity in the presence of boundaries, the BRST-invariant boundary value problem for the gauge field…
In this paper, we derive sharp asymptotics for the spectral data (eigenvalues and weight numbers) of the fourth-order linear differential equation with a distribution coefficient and three types of separated boundary conditions. Our methods…
The study of spectral properties of natural geometric elliptic partial differential operators acting on smooth sections of vector bundles over Riemannian manifolds is a central theme in global analysis, differential geometry and…
The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with…
The asymptotic expansion of the heat-kernel for small values of its argument has been studied in many different cases and has been applied to 1-loop calculations in Quantum Field Theory. In this thesis we consider this asymptotic behavior…
In this paper we continue the analysis of spectral problems in the setting of complete manifolds with fibred boundary metrics, also referred to as $\phi$-metrics, as initiated in our previous work. We consider the Hodge Laplacian for a…
We consider the Hodge Laplacian on manifolds with incomplete edge singularities, with infinite dimensional von Neumann spaces and intricate elliptic boundary value theory. We single out a class of its algebraic self-adjoint extensions. Our…
We consider the heat-kernel on a manifold whose boundary is piecewise smooth. The set of independent geometrical quantities required to construct an expression for the contribution of the boundary discontinuities to the C_{2} heat-kernel…