Related papers: A note on the functional determinant of higher-der…
We show that isotropic positive definite functions on the $d$-dimensional sphere which are $2k$ times differentiable at zero have $2k+[(d-1)/2]$ continuous derivatives on $(0,\pi)$. This result is analogous to the result for radial positive…
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…
We present a simple formalism for the evaluation of the Casimir energy for two spheres and a sphere and a plane, in case of a scalar fluctuating field, valid at any separations. We compare the exact results with various approximation…
An explicit formula to compute the multiplicative anomaly or defect of $\zeta$-regularized products of linear factors is derived, by using a Feynman parametrization, generalizing Shintani-Mizuno formulas. Firstly, this is applied on…
We consider the quantum effective action of Dirac fermions on four dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat…
We study the dimensional asymptotics of the effective actions, or functional determinants, for the Dirac operator D and Laplacians \Delta +\beta R on round S^n. For Laplacians the behavior depends on ``the coupling strength'' \beta, and one…
The functional determinant for a Coulomb potential (or mass squared) on a three-sphere is computed numerically.
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…
The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially…
In this paper, we compute the effective action of both a scalar field and a Dirac spinor field in the global de Sitter space of any dimension $d$ using the in-/out-state formalism. We show that there is particle production in even…
We investigate the effective action of 2+1 dimensional charged spin 1/2 fermions and spin 0 bosons in the presence of a $U(1)$ gauge field. We evaluate terms in an expansion up to second order in derivatives of the field strength, but…
The Hodge--de Rham Laplacian on spheres acting on antisymmetric tensor fields is considered. Explicit expressions for the spectrum are derived in a quite direct way, confirming previous results. Associated functional determinants and the…
The activation gap $\Delta$ of the fractional quantum Hall states at constant fillings $\nu =2/3$ and 2/5 has been measured as a function of the perpendicular magnetic field $B$. A linear dependence of $\Delta$ on $B$ is observed while…
We provide a list of equivalent conditions under which an additive operator acting on a space of smooth functions on a compact real interval is a multiple of the derivation.
We work with $\phi^4$ theory and study the 4PI effective action at 3-loop order. We discuss the relationship between the equations of motion obtained by taking functional derivatives of the effective action with respect to the variational…
New techniques for evaluating the closed time path action for non-equilibrium quantum fields are presented. A derivative expansion is performed using a proper time kernel. Applications relevant to the scalar field theory of warm inflation…
In this paper we study the action of pseudo-differential operators acting on Gevrey spaces. We introduce classes of classical symbols with spatial Gevrey regularity. As the spatial Gevrey regularity of a symbol $p(\cdot,\xi)$ may depend on…
We consider fermion (or determinantal) random point fields on Euclidean space $\mbR^d$. Given a bounded, translation invariant, and positive definite integral operator $J$ on $L^2(\mbR^d)$, we introduce a determinantal interaction for a…
In this paper, we investigate the relationship between positive definite functions on the unit sphere $\sph$ and on the Euclidean space $\RR^d$. For the dimension $d$ to be odd, a new technique is developed to establish the inheritance of…
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…