Related papers: Zeta function regularization in Casimir effect cal…
For a general Fuchsian group of the first kind with an arbitrary unitary representation we define zeta functions related to the contributions of the identity, hyperbolic, elliptic and parabolic conjugacy classes in Selberg's trace formula.…
We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…
By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the…
The Riemann zeta function regularization is employed to extract finite temperature corrections to effective magnetic moment $S^*$ of one- and two-dimensional Heisenberg ferro- and antiferromagnets. Whereas for the one-dimensional…
This article aims to examine the Casimir effect in the framework of stochastic semi-classical gravity. We commence with the semi-classical Einstein-Langevin equation, which introduces a first-order correction to the semi-classical gravity…
An exact formula that relates standard zeta functions and so-called hatted zeta functions in all orders of perturbation theory is presented. This formula is based on the Landau-Khalatnikov-Fradkin transformation
The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of…
The renormalization of MZV was until now carried out by algebraic means. We show that renormalization in general, of the multiple zeta functions in particular, is more than mere convention. We show that simple calculus methods allow us 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 consider analytic functions of the Riemann zeta type, for which, if $s$ is a zero, so is $1-s$. We use infinite product representations of these functions, assuming their zeros to be of first order. We use exponential factors to…
It has been argued since 1948, when it was experimentally demonstrated, that the Casimir effect-where two non-charged conducting plates have a weak but measurable force on each other dependent on the inverse fourth power of the distance…
So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for…
The problem of minimization of the least squares functional with a smooth, lower semi-continuous, convex regularizer $J(\cdot)$ is considered to be solved. Over some compact and convex subset $\Omega$ of the Hilbert space $\mathcal{H},$ the…
Summations and relations involving the Hurwitz and Riemann zeta-functions are extended first to Barnes zeta-functions and then to zeta-functions of general type. The analysis is motivated by the evaluation of determinants on spheres which…
We re-evaluate the zero point Casimir energy for the case of a massive scalar field in $\mathbf{R}^{1}\times\mathbf{S}^{3}$ space, allowing also for deviations from the standard conformal value $\xi =1/6$, by means of zero temperature zeta…
We apply the recently developed method of differential renormalization to the Wess-Zumino model. From the explicit calculation of a finite, renormalized effective action, the $\beta$-function is computed to three loops and is found to agree…
We utilize an effective field theory approach to calculate Casimir interactions between objects bound to thermally fluctuating fluid surfaces or interfaces. This approach circumvents the complicated constraints imposed by such objects on…
The paper deals with Hawking radiation related to non-static spherically symmetric black hole. Quantum corrections are incorporated using Hamilton-Jacobi method beyond semi-classical approximation. It is found that different order…
The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would…
The Casimir force provides a striking example of the effects of quantum fluctuations in a mesoscopic system. Because it arises from the objects' electromagnetic response, the necessary calculations in quantum field theory are most naturally…