Related papers: Heat-kernel coefficients and functional determinan…
A Hermite type formula is introduced and used to study the zeta function over the real and complex n-projective space. This approach allows to compute the residua at the poles and the value at the origin as well as the value of the…
For an elliptic differential operator $D$ of order $h$ in $n$ dimensions, the spectral $\zeta$-function $\zeta_D(s)$ for $\Re s > \frac{n}{h}$ can be evaluated as an integral over the heat kernel $e^{-t D}$. Here, alternative expressions…
An asymptotic expansion of the trace of the heat kernel on a cone where the heat coefficients have a delta function behavior at the apex is obtained. It is used to derive the renormalized effective action and total energy of a…
The scalar functional determinants on sectors of the two-dimensional disc and spherical cap are determined for arbitrary angles (rational factors of $\pi$). The wholesphere and hemisphere expressions are also given, in low dimensions, for…
We suggest a method of reduction of mixed absolute and relative boundary conditions to pure ones. The case of rank two tensor is studied in detail. For four-dimensional disk the corresponding heat kernel is expressed in terms of scalar heat…
We derive the asymptotic expansion of the heat kernel for a Laplace operator acting on deformed spheres. We calculate the coefficients of the heat kernel expansion on two- and three-dimensional deformed spheres as functions of deformation…
We investigate the short-time expansion of the heat kernel of a Laplace type operator on a compact Riemannian manifold and show that the lowest order term of this expansion is given by the Fredholm determinant of the Hessian of the energy…
We present results for the fermion determinant in an external Yukawa-coupled scalar field, a quantity relevant to instanton and sphaleron transition rates as well as bubble nucleation occuring in the electroweak phase transition when the…
We present a technique to calculate the spin relaxation of hot electrons during their energy thermalization in the Gamma-valley of zinc-blende semiconductors. The results of this model match recent experimental data and they can be used to…
We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the…
We report the calculation of the fourth coefficient in an expansion of the heat kernel of a non-minimal, non-abelian kinetic operator in an arbitrary background gauge in arbitrary space-time dimension. The fourth coefficient is shown to…
Explicit formulas for the zeta functions $\zeta_\alpha (s)$ corresponding to bosonic ($\alpha =2$) and to fermionic ($\alpha =3$) quantum fields living on a noncommutative, partially toroidal spacetime are derived. Formulas for the most…
We study a system composed of a quantum dot in contact with ferromagnetic leads, held at different temperatures. Spin analogues to the thermopower and thermoelectric figures of merit are defined and studied as a function of junction…
Two multiplicative anomalies are evaluated for the determinant of the conformal higher spin propagating operator on spheres given by Tseytlin. One holds for the decomposition of the higher derivative product into its individual second order…
We bring together two apparently disconnected lines of research (of mathematical and of physical nature, respectively) which aim at the definition, through the corresponding zeta function, of the determinant of a differential operator…
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 give concrete descriptions of leafwise cohomology groups and show the regularized determinant expression of the dynamical zeta function for fiber bundles over $S^{1}$. As applications, we show a functional equation and…
An expansion in the number of spatial covariant derivatives is carried out to compute the $\zeta$-function regularized effective action of 2+1-dimensional fermions at finite temperature in an arbitrary non-Abelian background. The real and…
We express the zeta function associated to the Laplacian operator on $S^1_r\times M$ in terms of the zeta function associated to the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulas for the…
The spectral zeta function of the Laplacian on self-similar fractal sets has been previously studied and shown to meromorphically extend to the complex plane. In this work we establish under certain conditions a relationship between the…