5 research outputs found
The ubiquitous -function and some of its "usual" and "unusual" meromorphic properties
In this contribution we announce a complete classification and new exotic
phenomena of the meromorphic structure of \z-functions associated to conic
manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic
extensions of these \z-functions have, in general, countably many logarithmic
branch cuts on the nonpositive real axis and unusual locations of poles with
arbitrarily large multiplicity. Moreover, we give a precise
algebraic-combinatorial formula to compute the coefficients of the leading
order terms of the singularities.Comment: Paper presented at the 8th Workshop on Quantum Field Theory under the
Influence of External Conditions (Leipzig, Germany, 16-21 September, 2007
Vacuum Expectation Value of the Spinor Massive field in the Cosmic String Space-Time
We found the contribution to the vacuum expectation value of the
energy-momentum tensor of a massive Dirac field due to the conical geometry of
the cosmic string space-time. The heat kernel and heat kernel expansion for the
squared Dirac operator in this background are also considered and the first
three coefficients were found in an explicity form.Comment: 9 pages, 1 figure (2 ref added) (enlarged version
Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
In this article we consider the zeta regularized determinant of Laplace-type
operators on the generalized cone. For {\it arbitrary} self-adjoint extensions
of a matrix of singular ordinary differential operators modelled on the
generalized cone, a closed expression for the determinant is given. The result
involves a determinant of an endomorphism of a finite-dimensional vector space,
the endomorphism encoding the self-adjoint extension chosen. For particular
examples, like the Friedrich's extension, the answer is easily extracted from
the general result. In combination with \cite{BKD}, a closed expression for the
determinant of an arbitrary self-adjoint extension of the full Laplace-type
operator on the generalized cone can be obtained.Comment: 27 pages, 2 figures; to appear in Manuscripta Mathematic