Related papers: Spinors and forms on generalised cones
A systematic presentation of spinors in various dimensions is given.
We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For…
Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation…
A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over the…
In this paper, we study the generalized Clifford-Fourier transform introduced in [6] using the Laplace transform technique. We give explicit expressions in the even dimensional case, we obtain polynomial bounds for the kernel functions and…
Using the characterization of the spin representation in terms of exterior forms, we give a complete classification of invariant spinors on the nine homogeneous realizations of the sphere $S^n$. In each of the cases we determine the…
We obtain optimal estimates of the Poincar\'e constant of central balls on manifolds with finitely many ends. Surprisingly enough, the Poincar\'e constant is determined by the second largest end. The proof is based on the argument by…
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…
We give a spinorial characterization of isometrically immersed surfaces into 3-dimensional homogeneous manifolds with 4-dimensional isometry group in terms of the existence of a particular spinor, called generalized Killing spinor. This…
Number sequences with wide-ranging applications in mathematics, physics, medicine, and engineering remain an active research topic. This study examines these sequences through the general framework of Horadam numbers and their special cases…
We give a spinorial characterization of isometrically immersed hypersurfaces into 4-dimensional space forms and product spaces $\M^3(\kappa)\times\R$, in terms of the existence of particular spinor fields, called generalized Killing spinors…
Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the…
We employ the polar re-formulation of spinor fields to see in a new light their classification into regular and singular spinors, these last also called flag-dipoles, further splitting into the sub-classes of dipoles and flagpoles: in…
In this paper, we study the geometry associated with Schroedinger operator via Hamiltonian and Lagrangian formalism. Making use of a multiplier technique, we construct the heat kernel with the coefficient matrices of the operator both…
We study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the…
We study the spectral properties of the Laplace type operator on the circle. We discuss various approximations for the heat trace, the zeta function and the zeta-regularized determinant. We obtain a differential equation for the heat kernel…
We investigate the generalized form factors of the nucleon in a light-cone spectator-diquark model. Compared to the form factors, the generalized form factors contain some more information of the structure of the nucleon. In our…
We develop a new framework for the study of generalized Killing spinors, where generalized Killing spinor equations, possibly with constraints, can be formulated equivalently as systems of partial differential equations for a polyform…
We explicitly calculate the moments $t_n$ of general Heisenberg Hamiltonians up to eighth order. They have the form of finite sums of products of two factors. The first factor is represented by a (multi-)graph which has to be evaluated for…
We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…