Email: Andrei.Khrennikov@msi.vxu.se
Main publications:
1. "p-adic valued distributions in mathematical physics." Kluwer Academic Publishers, Dordrecht, 1994.
2. "Non-Archimedean analysis: quantum paradoxes, dynamical systems and biological models." Kluwer Academic Publishers, Dordrecht, 1997.
3. "Superanalysis", Nauka, Moscow, 1997 (in Russian).
Research: I work in three main directions: (a) p-adic analysis and applications to quantum physics, dynamical systems and biology; (b) infinite-dimensional analysis with applications to quantum field theory (especially Feynman integration); (c) superanalysis (analysis of functions and distributions) with anticommuting variables with applications to quantum theory of superfields (especially Feynman integration).
In the domain (a) I study
1) differential and pseudo-differential equantions over non-Archimedean number fields in the framework of the corresponding theory of distributions;
2) non-Kolmogorovean probabilistic models with p-adic probabilities which are defined on the frequancy basis as limits of relative frequencies with respect to p-adic topologies (this gives us a possibility to realize negative probability distributions on the frequency basis); p-adic probability investigations are closely connected with works of R.von Mises and Kolmogorov´s theory of the algorithmic complexity; in fact I hope that such a change of the Kolmogorov axiomatics (1933) of the probability theory might play for physics a role which is similar to the role of Lobachevslii geometrical model.
3) quantum models over p-adic space-time; in this framework we interpret p-adic numbers as giving a finite precision for quantum measurements (and the real as giving an infinite one);
4) p-adic negative probability distributions are used to provide solutions for some quantum paradoxes; in particular, Einstein-Podolsky-Rosen paradox.
5) dynamical systems over p-adic fields with applications for describing the process of thinking: "the system conscious- subconscious as a p-adic dynamical processor."
6) p-adic dynamical systems for social sciences.
In the field (b) I study:
1) distributions on infinite-dimenasional spaces (the Feynman "measure" is an important example of such a distribution;
2) pseudo-differential and differential operators;
3) stochastic processes.
The similar things are studied in the field (c).