On the Mathematical Structure of a Large Class of Physical Theories,
POLITECNICO DI MILANO (ITALY) ISTITUTO DI MATEMATICA
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Many physical theories show formal similarities due to the existence of a common mathematical structure. This structure is independent of the physical contents of the theory and can be found in classical, relativistic and quantum theories for discrete and continuous systems. In particular many field theories of different tensorial order exhibit such a structure. Traditionally the study of similar structures is the subject of the mathematical field theory. Its starting point is the existence of an action principle from which field equations are deduced. Field theory is particularly suitable for fundamental theories as electromagnestism, gravitation and quantum theories. The approach in the paper is based on a different point of view the author ascertains the existence of a decomposition of the fundamental equation into three sets of equations. Typically these are balance, definition and constitutive equations.
- Numerical Mathematics