Related papers: Heat-kernel coefficients and functional determinan…

A magnetic monopole is placed at the centre of a 3-ball whose surface, S, is tiled by the symmetry group, G, of a regular solid. The quantum mechanics on the two-dimensional quotient, S/G, is developed and the monopole charge is found to be…

The standard formula for the change in the effective action under a conformal transformation is extended to the case when the boundary is piecewise smooth. We then find the functional determinants of the scalar Laplacian on regions of the…

Let K be a field of characteristic 0 and A be a rigid tensor K-linear category. Let M be a finite-dimensional object of A in the sense of Kimura-O'Sullivan. We prove that the "motivic" zeta function of M with coefficients in K\_0(A) has a…

From spinor and scalar 2+1 dimensional QED effective actions at finite temperature and density in a constant magnetic field background, we calculate the corresponding virial coefficients for particles in the lowest Landau level. These…

We present a pedagogical exposition of some applications of functional methods in quantum field theory: we use heat-kernel and zeta-function techniques to study the Casimir effect, the pair production in strong electric fields, quantum…

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the…

The charge and spin-dependent thermoelectric responses are investigated on a single-helical molecule possessing a collinear antiferromagnetic spin arrangement with zero net magnetization in the presence of a transverse electric field. Both…

We study the zeta-function regularization of functional determinants of Laplace and Dirac-type operators in two-dimensional Euclidean $AdS_2$ space. More specifically, we consider the ratio of determinants between an operator in the…

The purpose of this paper is to investigate coefficient matrices of functional equations of zeta functions associated with homogeneous cones, which are given explicitly in the previous paper, in detail. We prove that the coefficient matrix…

This is a quick review on some technology concerning the local zeta function applied to Quantum Field Theory in curved static (thermal) spacetime to regularize the stress-energy tensor and the field fluctuations.

We calculate the low-temperature thermodynamic quantities (magnetization, correlation functions, transverse and longitudinal correlation lengths, spin susceptibility, and specific heat) of the frustrated one-dimensional spin-half J1-J2…

We compute the heat kernel coefficients that are needed for the regularization and renormalization of massive gravity. Starting from the Stueckelberg action for massive gravity, we determine the propagators of the different fields (massive…

In the Majorana representation of a spin 1/2 we find an identity which relates spin-spin correlators to one-particle fermionic correlators. This should be contrasted with the straightforward approach in which two-particle (four-fermion)…

We define a zeta function of a graph by using the time evolution matrix of a general coined quantum walk on it, and give a determinant expression for the zeta function of a finite graph. Furthermore, we present a determinant expression for…

We further develop the new approach, proposed in part I (hep-th/9807072), to computing the heat kernel associated with a Fermion coupled to vector and axial vector fields. We first use the path integral representation obtained for the heat…

The asymptotic expansion of the heat-kernel for small values of its argument has been studied in many different cases and has been applied to 1-loop calculations in Quantum Field Theory. In this thesis we consider this asymptotic behavior…

In this article, we study special values of the Dedekind zeta function over an imaginary quadratic field. The values of the Dedekind zeta function at any even integer over any totally real number field is quite well known in literature. In…

This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel…

We investigate analytic properties of height zeta functions of toric varieties. Using the height zeta functions, we prove an asymptotic formula for the number of rational points of bounded height with respect to an arbitrary line bundle…

Cluster perturbation theory is applied to the two-dimensional Hubbard $t-t'-t''-U$ model to obtain doping and temperature dependent electronic spectral function with $4 \times 4$ and 12-site clusters. It is shown that evolution of the…