๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Partition functions and Jacobi fields in the Morse theory

โœ Scribed by Soon-Tae Hong

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
114 KB
Volume
48
Category
Article
ISSN
0393-0440

No coin nor oath required. For personal study only.

โœฆ Synopsis

We study the semiclassical partition function in the frame work of the Morse theory, to clarify the phase factor of the partition function and to relate it to the eta invariant of Atiyah. Converting physical system with potential into a curved manifold, we exploit the Jacobi fields and their corresponding eigenvalues of the Sturm-Liouville operator to be associated with geodesics on the curved manifold and with the Hamilton-Jacobi theory.

๐Ÿ“œ SIMILAR VOLUMES

The Partition Function for Topological F
The Partition Function for Topological Field Theories
โœ J. Gegenberg; G. Kunstatter ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 685 KB

We use a Hodge decomposition and its generalization to non-abelian flat vector bundles to calculate the partition function for abelian and non-abelian BF theories in \(n\) dimensions. This enables us to provide a simple proof that the partition function is related to the Ray-Singer torsion defined o

Eigenvalue independent partitioning and
Eigenvalue independent partitioning and direct minimization in self-consistent field theory
โœ J.A.R. Coope; D.W. Sabo ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 351 KB

It is pointed out that the matrk eIements of a partitioning operator, f, introduced previously for constructing effective hamiltonians, provide natural sets of unconstrained and non-redundant variables in which to formulate self-consistent fieield theory. The elements offare complementary to corresp