Accession Number : AD0765048

Title :   A Mathematical Model for Physical Theories. Nota I and II,

Corporate Author : POLITECNICO DI MILANO (ITALY) ISTITUTO DI MATEMATICA

Personal Author(s) : Tonti,Enzo

Report Date : 1972

Pagination or Media Count : 18

Abstract : Many physical theories exhibit a common mathematical structure that is independent of the physical contents of the theory and is common to discrete and continuum theories, be they of classic, relativistic or quantum nature. The starting point of this structure is the possibility of decomposing the fundamental equation of many physical theories in three equations, known in classical fields of the macrocosm as definition, balance and constitutive equations, whose operators enjoy peculiar properties. The properties are as follows: the operator of balance equation is the adjoint, with respect to an opportune bilinear functional, of the operator of definition equation (if the last is linear) or of its Gateaux derivative (if it is nonlinear). Moreover, the operator of constitutive equation is symmetric (when it is linear) or has symmetric Gateaux derivative (when it is nonlinear). Such a peculiar decomposition permits us to obtain a profound introspection into the mathematical structure of a theory. The fact that this decomposition can be achieved in a large number of physical theories and the fact that when it exists we can deduce easily a large number of mathematical properties, suggest constructing a mathematical model for physical theories.

Descriptors :   (*MATHEMATICAL MODELS, PHYSICS), MAPPING(TRANSFORMATIONS), FIELD THEORY, TOPOLOGY, THEOREMS, ITALY

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE