START
DATE: 2007-06-01 DURATION:
36 month(s) + 4 months
extension.

DESCRIPTION:

In a word, this
project plans to study applications of infinite dimensional
analysis ( Gaussian and Poisson) and its perturbations to
statistical mechanics and quantum field theory through
Gibbs states and Feynman integrals, respectively.

ABSTRACT:

In a word, this
project plans to study applications of infinite dimensional
analysis ( Gaussian and Poisson) and its perturbations to
statistical mechanics and quantum field theory through
Gibbs states and Feynman integrals,
respectively.

ON
THE POISSON ANALYSIS WE PLAN:

- jump type and
birth and dead type dynamics in
continuum,

- large time
asymptotic of interacting jump type
process,

- characterize
invariant measures using the technique of Georgii for
diffusion dynamics,

- describe
physical systems with further internal degrees of freedom
through the concept of marked
configurations.

ON
THE FEYNMAN INTEGRALS WE PLAN:

- Combining the
harmonic oscillator with the Westerkamp--Kuna class of
rapidly growing potentials. The construction of the
corresponding

- Feynman
integrands is in particular of interest for going into the
direction of quantum field theory,

- In particular
we plan to identify tau-functionals, i.e. the generating
functional of time ordered (field) expectations as Fourier
Gauss transforms of White Noise
distributions.

- Realizing and
generalizing the complex scaling ansatz of Doss for
constructing solutions to the Schrödinger
equation.

- We emphasize
that as a particular goal of this research we intend to
develop methods for models where as in quantum field theory
perturbation expansions fail to exist.

MAIN
AREA:

Mathematics/Physics