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Volume 12: Pages 61-79, 1999
Electromagnetic‐Like Generation of Unified‐Gauge Theories
R. Mignani 1, E. Pessa 2, G. Resconi 3
1Dipartimento di Fisica “E. Amaldi”, Università di Roma “Roma Tre”, Via della Vasca Navale, 84, I‐00146 Roma, Italy and I.N.F.N.—Sezione di Roma Tre
2ECONA—Interuniversity Centre for Research on Cognitive Processing in Natural and Artificial Systems, c/o Dipartimento di Psicologia, I Universitá di Roma “La Sapienza”, Via dei Marsi, 78, I‐00185 Roma, Italy
3Dipartimento di Matematica, Università Cattolica del Sacro Cuore, Via Trieste, 17, 25121 Brescia, Italy
We carry out a critical analysis of the Maxwell electromagnetic theory, with emphasis on its “geometrical” features and gauge‐theoretical properties. This allows us to single out five fundamental principles, which are at the very foundation of electromagnetism and can be used to build up any (electromagnetic‐like) unified‐gauge theory. Such principles are essentially based on the different order of commutators among covariant derivatives, and are connected in a natural way to the commutative diagrams of various orders, which relate the relevant operators involved in the electromagnetic theory. An application of this general procedure is given by considering general relativity, whose basic equations can also be derived from the five basic postulates. Moreover, the equations satisfied by the sources of the gauge field can be derived from a fundamental invariant by imposing that the continuity equation for the current be satisfied. Such an electromagnetic‐like generation scheme permits us to obtain a family of unified‐gauge theories, hierarchically arranged by increasing complexity.
Keywords: Maxwell electromagnetic theory, unified‐gauge theories, general relativity, system theory, commutative diagrams
Received: August 13, 1997; Published online: December 15, 2008