Statistical interpretation of p-adic-valued quantum field theory

Andrei Yu. Khrennikov

Branko G Dragovich

Andrei Yu. Khrennikov, Marcus Nilson

Andrew Khrennikov

The development of p-adic quantum mechanics has made it necessary to construct a probability theory in which the probabilities of events are p-adic numbers. The foundations of this theory are developed here. The frequency definition of probability is used. A general principle of statistical stabilization of relative frequencies is formulated. By virtue of this principle, statistical stabilization of relative frequencies, which are, like all experimental data, rational numbers, can be considered not only in the real topology but also in p-adic topologies.

C. Alacoque, Philippe Ruelle, E. Thiran +2 more

Andrei Yu. Khrennikov

This is a review about p‐adic valued probabilities, applications to quantum physics and cognitive sciences. We also do the next step in development of non‐Kolmogorovian models and consider an analogue of probability theory for probabilities taking values in topological groups. The main attention is paid to statistical interpretation of p‐adic probabilities as well as more general probabilities with values in topological groups.