Mathematics
Scientific paper
Mar 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978ncimb..44...67t&link_type=abstract
Nuovo Cimento, Sezione B, vol. 44B, Mar. 11, 1978, p. 67-98.
Mathematics
15
Field Theory (Physics), Relativity, Space-Time Functions, Conservation Laws, Electromagnetic Fields, Flux Density, Formalism, Gravitation Theory, Manifolds (Mathematics), Momentum, Vector Analysis
Scientific paper
A generalization of the formalism of classical field theory is obtained by replacing the space-time manifold M by the ten-dimensional manifold S of all the local reference frames. The geometry of the manifold S is determined by ten vector fields corresponding to ten operationally defined infinitesimal transformations of the reference frames. The action principle is written in terms of a differential 4-form in the space S (the Lagrangian form). Differential 3-forms in S are used to represent densities and currents. The action principle is employed to derive the field equations and to establish the connection between symmetries and conservation laws (Noether's theorem). The concepts are used to reformulate Einstein's theory of gravitation and Maxwell's theory of electromagnetism. It is pointed out that the general formalism can also be used to formulate theories in which charge, energy, and momentum cannot be localized in space-time.
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