Please use this identifier to cite or link to this item:
|Scopus||Web of Science®||Altmetric|
|Title:||Heat kernel asymptotics, path integrals and infinite-dimensional determinants|
|Citation:||Journal of Geometry and Physics, 2018; 131:66-88|
|Abstract:||We compare the short-time expansion of the heat kernel on a Riemannian manifold with the formal stationary phase expansion of its representing path integral and prove that these asymptotic expansions coincide. Besides shedding light on the formal properties of quantum mechanical path integrals, this shows that the lowest order term of the heat kernel expansion is given by the Fredholm determinant of the Hessian of the energy functional on the space of finite energy paths. We also relate this to the zeta determinant of the Jacobi operator, considering both the near-diagonal asymptotics as well as the behavior at the cut locus.|
|Keywords:||Path integrals; heat kernels; heat kernel asymptotics; Fredholm determinant; zeta function; zeta determinant|
|Rights:||© 2018 Elsevier B.V. All rights reserved.|
|Appears in Collections:||Mathematical Sciences publications|
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.