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- W1580496021 abstract "The observation and the discussion of the physical reality of phenomena, leads to bring out concepts which have to be described in a non ambiguous mathematical language. Concerning Dirac's calculus we shall introduce, besides the usual definitions for the concepts of point, number, function etc ... , additional concepts for the physical point, the physical equalities, physical infinities and infinitesimals ... etc ... In particular we introduce a new equality $=^{D}$, called Dirac-equality, which differs as well from the classical equality as from the weak equalities introduced in various theories of generalized functions. All these definitions are based on a definition in the language of Relative Set Theory of the metaconcepts of improperness used by P.A.M. Dirac in [Di], when he claimed textit{Strictly of course, $delta(x)$ is not a proper function of $x$, ... , ... $delta'(x), delta''(x)$.... are even more discontinuous and less proper than $delta(x)$ itself}. We defined this way a concept of observed derivative which extends the usual one to a large class of textit{discontinuous} possibly non-standard functions. All the multiplications of improper or very improper functions, including the delta-functions and their observed derivatives, are obviously allowed. Now the problem of the multiplication is replaced by another one: under which conditions is the Dirac-equality of two functions preserved by a multiplication term by term?" @default.
- W1580496021 created "2016-06-24" @default.
- W1580496021 creator A5083711535 @default.
- W1580496021 date "2007-01-01" @default.
- W1580496021 modified "2023-10-11" @default.
- W1580496021 title "A mathematical framework for Dirac's calculus" @default.
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- W1580496021 doi "https://doi.org/10.36045/bbms/1170347823" @default.
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