Spinors and forms on the ball and the generalized cone

Abstract

A method is presented, and used, for determining any heat-kernel coefficient for the form-valued Laplacian on the jD-ball as an explicit function of dimension and form order. The calculation is offerred as a particular application of a general technique developed earlier for obtaining heat-kernel coefficients on a bounded generalized cone which involves writing the sphere and ball C _ functions, and coefficients, in terms of Barnes ("-functions and generalized Bernoulli polynomials. Functional determinants are computed. Spinors are also treated by the general method.

Chiral bag boundary conditions on the ball

“…The above results resemble very much the structure of the results found for different boundary conditions given in [23,[29][30][31][32]. In particular, a reduction of the analysis from the ball to the sphere (in form of the Barnes zeta functions) has been achieved.…”

“…In particular, a reduction of the analysis from the ball to the sphere (in form of the Barnes zeta functions) has been achieved. Indeed, instead of using the presented algorithm we could equally well have used the contour integral method developed in [33,29,30]. The starting point for the zeta function associated with the eigenvalues from (1.7) in this approach reads…”

Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone

“…In particular, in one dimension rather general and elegant results may be obtained, which has attracted the interest of mathematicians especially in the last decade or so [21,22,51,60,61,82,83,84]. In higher dimensions known results are restricted to highly symmetric configurations [13,14,16,23,44,45,46,50] or conformally related ones [10,11,16,47,48].…”

p-forms on d-spherical tessellations

“…Although the expression, (14), for ζ CE b (p, s) is valid just for the middle rank forms on S d /Γ, it has significance for all p when the factored sphere is realised as the base of a generalised cone in R d+1 , [11], [12]. I have also referred to this construction as a bounded Möbius corner, [1,13].…”