
We encode dynamical symmetries of Born-Infeld theory in a geometry on the tangent bundle of generally curved spacetime manifolds. The resulting covariant formulation of a maximal acceleration extension of special and general relativity is put to use in the discussion of particular point particle dynamics and the transition to a first quantized theory.
39 pages, 1 figure, LaTeX, minor corrections (journal version)
High Energy Physics - Theory, Special relativity, Noncommutative geometry (à la Connes), FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Relativistic gravitational theories other than Einstein's, including asymmetric field theories, General Relativity and Quantum Cosmology, special and general relativity, High Energy Physics - Theory (hep-th), Born-Infeld theory, first quantized theory, Quantization of the gravitational field, curved spacetime manifolds
High Energy Physics - Theory, Special relativity, Noncommutative geometry (à la Connes), FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Relativistic gravitational theories other than Einstein's, including asymmetric field theories, General Relativity and Quantum Cosmology, special and general relativity, High Energy Physics - Theory (hep-th), Born-Infeld theory, first quantized theory, Quantization of the gravitational field, curved spacetime manifolds
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