A Mathematical Model for Physical Theories. Nota I and II,
POLITECNICO DI MILANO (ITALY) ISTITUTO DI MATEMATICA
Pagination or Media Count:
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.
- Theoretical Mathematics