Recent Results in Infinite Dimensional Analysis and Applications to Feynman Integrals

Details Recent Results in Infinite Dimensional Analysis and Applications to Feynman Integrals Recent Results in Infinite Dimensional Analysis and Applications to Feynman Integrals

2003-02-28

arxiv.org/abs/math-ph/0302066v1

Physics

Mathematical Physics

140 pages Thesis Uni Bielefeld

Scientific paper

The first part of this thesis proposes a general approach to infinite dimensional non-Gaussian analysis, including the Poissonian case. In particular distribution theory is developed. Using appropriate integral transformations, generalized and test functionals are characterized in terms of holomorphy. Furthermore differential operators, Wick product and change of measure are discussed. In the second part the Gaussian case (White Noise Analysis) is worked out in more detail. Furthermore operators on distribution spaces e.g. compositions with shifts and complex scaling are discussed. In the third part Feynman integrals are constructed using White Noise distributions as integrands. Its expectation yields the path integral. This rigorous approach is applied to the interacting case. A generalization of the Khandekar Streit method is proposed. The resulting class of admissible potentials covers signed measures. The Albeverio Hoegh-Krohn class, which consists of Fourier transforms of measures, is discussed. The third approach is based on complex scaling. The so-called Doss class allows analytic potentials which obey some growth condition. Using the White Noise calculus of differential operators, the functional form of the canonical commutation relation is derived. Finally Ehrenfest's theorem is proven.

Affiliated with

Also associated with

No associations

Rating

Recent Results in Infinite Dimensional Analysis and Applications to Feynman Integrals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Recent Results in Infinite Dimensional Analysis and Applications to Feynman Integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Recent Results in Infinite Dimensional Analysis and Applications to Feynman Integrals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-643678