Related papers: Antisymmetric tensor fields on spheres: functional…
We show that in any harmonic space, the eigenvalue spectra of the Laplace operator on small geodesic spheres around a given point determine the norm $|\nabla R|$ of the covariant derivative of the Riemannian curvature tensor in that point.…
We give optimal bounds for the radial, space and time derivatives of arbitrary order of the heat kernel of the Laplace--Beltrami operator on Damek--Ricci spaces. In the case of symmetric spaces of rank one, these complete and actually…
We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti-de Sitter. In particular, we explicitly identify higher order counterterms, which…
We compute the gravitational effective action by integrating out quantum matter fields in a weak gravitational field, using the Schwinger-Keldysh (in-in) formalism. We pay particular attention to the role of the initial quantum state in the…
The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for…
A direct analog of Hadamard's three-circle theorem is obtained for harmonic functions (in weighted L^2-norm) in case of (n-1)-dimensional non-concentric spheres in R^n. The result extends the concentric case to correlated non-concentric,…
We consider modeling for strong-strong beam-beam interactions beyond preceding linearized/perturbative methods such as soft gaussian approximation or FMM (HFMM) etc. In our approach discrete coherent modes, discovered before, and possible…
We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and…
This paper aims to study the asymptotic behaviour of the fundamental solutions (heat kernels) of non-local (partial and pseudo differential) equations with fractional operators in time and space. In particular, we obtain exact asymptotic…
Heat-kernel expansion and zeta function regularisation are discussed for Laplace type operators with discrete spectrum in non compact domains. Since a general theory is lacking, the heat-kernel expansion is investigated by means of several…
In the present paper we consider two related problems, i.e. the description of geodesics and the calculation of the spectrum of the Laplace-Beltrami operator on a flag manifold. We show that there exists a family of invariant metrics such…
The aim of this article is to calculate (to first order in $\hbar$) the renormalized effective action of a self interacting massive scalar field propagating in the space-time due to a cylindrically symmetric, rotating body. The vacuum…
We perform Hartree calculations of symmetric and asymmetric semi-infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature. In addition to the…
We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection…
In the present paper we show properties of a little-known Laplacian operator acting on symmetric tensors. This operator is an analogue of the well known Hodge-de Rham Laplacian which acts on exterior differential forms. Moreover, this…
A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics…
The relation between solutions to Helmholtz's equation on the sphere $S^{n-1}$ and the $[{\gr sl}(2)]^n$ Gaudin spin chain is clarified. The joint eigenfuctions of the Laplacian and a complete set of commuting second order operators…
We show that the action of conformal vector fields on functions on the sphere determines the spectrum of the Laplacian (or the conformal Laplacian), without further input of information. The spectra of intertwining operators (both…
We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function…
The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…