6. R. Mignani, E. Pessa, G. Resconi, Electromagnetic‐Like Generation of Unified‐Gauge Theories

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Volume 12: Pages 61-79, 1999

ElectromagneticLike Generation of UnifiedGauge 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, I00146 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, I00185 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 gaugetheoretical 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 (electromagneticlike) unifiedgauge 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 electromagneticlike generation scheme permits us to obtain a family of unifiedgauge theories, hierarchically arranged by increasing complexity.

Keywords: Maxwell electromagnetic theory, unifiedgauge theories, general relativity, system theory, commutative diagrams

Received: August 13, 1997; Published online: December 15, 2008