Traditionally, all constructions of mathematical physics were carried out over the field of real numbers R. However, a different point of view is also possible according to which on fantastically small distances (of order 10−33) the space-time has non-Archimedean structure and, consequently, cannot be described by real numbers. The philosophy and ideology of non-Archimedean physics were laid as a foundation by I.V. Volovich (1987), he also advanced an invariance principle (which got the name of the Volovich invariance principle). By virtue of this principle, rational numbers formed the experimental basis for any physical formalism, and physical formalism must be invariant with respect to the choice of the completion of the field of rational numbers. Thus, along with real physical theories, certain theories were worked out over other number fields, in particular, over fields of p-adic numbers (see ).
KeywordsCauchy Problem Quadratic Extension Parseval Equality Archimedean Case Strong Triangle Inequality
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