Related papers: Spectral functions in mathematics and physics
We establish dimension-independent estimates related to heat operators e^{tL} on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates…
Quantum-mechanical system -- spin 1 particle in external Coulomb field is studied on the base of the matrix Duffin-Kemmer-Petiau formalism with the use of the tetrad technique. Separation of the variables is performed with the help of…
We first prove Kato's inequalities for the Laplacian and a Schr$\ddot{o}$dinger-type operator on smooth functions on closed Riemannian manifolds. We then apply the result to establish some new domination inequalities for spectral zeta…
We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…
We use the functorial properties of Rieffel's pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are…
For fermionic fields on a compact Riemannian manifold with boundary one has a choice between local and non-local (spectral) boundary conditions. The one-loop prefactor in the Hartle-Hawking amplitude in quantum cosmology can then be studied…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We discuss the vacuum energy of a quantized scalar field in the presence of classical surfaces, defining bounded domains $\Omega \subset {\mathbb{R}}^{d}$, where the field satisfies ideal or non-ideal boundary conditions. For the…
We discuss the problem of the spectral function of vacuum energy. In traditional approach the ultraviolet divergencies of the vacuum energy are cancelled by imposing relations between different quantum fields and their masses. The emergent…
In this paper, we study an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold without a boundary at enough small values of the proper time. The Seeley-DeWitt coefficients of this decomposition…
We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the…
In this paper we consider some analytical relations between gamma function $\Gamma(z)$ and related functions such as the Kurepa's function $K(z)$ and alternating Kurepa's function $A(z)$. It is well-known in the physics that the Casimir…
We consider the energy functional on the space of sections of a sphere bundle over a Riemannian manifold (M, <,>) equipped with the Sasaki metric and we discuss the characterising condition for critical points. Likewise, we provide a useful…
A precise zeta-function calculation shows that the contribution of the vacuum energy to the observed value of the cosmological constant can possibly have the desired order of magnitude albeit the sign strongly depends on the topology of the…
The survey summarizes briefly the results obtained recently in the Casimir effect studies considering the following subjects: i) account of the material characteristics of the media and their influence on the vacuum energy (for example,…
After a brief survey of zeta function regularization issues and of the related multiplicative anomaly, illustrated with a couple of basic examples, namely the harmonic oscillator and quantum field theory at finite temperature, an…
The single-particle spectral functions $A({\bf k},\omega)$ and self-energies $\Sigma({\bf k},\omega)$ are calculated within the $t-J$ model using the finite-temperature Lanczos method for small systems. A remarkable asymmetry between the…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
The nuclear spectral function at high missing energies and momenta has been determined from a self-consistent calculation of the Green's function in nuclear matter using realistic nucleon-nucleon interactions. The results are compared with…
In statistical mechanics one packages the possible energies of a system into a partition function. In number theory, and elsewhere in mathematics, one packages the spectrum of a phenomenon, say the prime numbers, into a $\zeta$-function or…