Numbers ..., natural, rational, real, complex, p-adic .... What do you
know about p-adic numbers? Probably, you have never used any p-adic
(nonrational) number before now. I was in the same situation few years
ago. p-adic numbers were considered as an exotic part of pure
mathematics without any application. I have also used only real and
complex numbers in my investigations in functional analysis and its
applications to the quantum field theory and I was sure that these
number fields can be a basis of every physical model generated by
nature. But recently new models of the quantum physics were proposed on
the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic
analysis, p-adic physics, p-adic probability? p-adic numbers were
introduced by K. Hensel (1904) in connection with problems of the pure
theory of numbers. The construction of Qp is very similar to the
construction of (p is a fixed prime number, p = 2,3,5, ...,127, ... ).
Both these number fields are completions of the field of rational
numbers Q. But another valuation 1 . Ip is introduced on Q instead of
the usual real valuation 1 . I- We get an infinite sequence of non
isomorphic completions of Q: Q2, Q3, ..., Q127, ..., IR = Qoo- These
fields are the only possibilities to com plete Q according to the famous
theorem of Ostrowsky.