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Matter, Fields, and Reparametrization-Invariant Systems

Vesselin G. Gueorguiev
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Abstract

We study reparametrization-invariant systems, mainly the relativistic particle and its D-dimensional extended object generalization--d-brane. The corresponding matter Lagrangians naturally contain background interactions, like electromagnetism and gravity. For a d-brane that doesn't alter the background fields, we define non-relativistic equations assuming integral sub-manifold embedding of the d-brane. The mass-shell constraint and the Klein-Gordon equation are shown to be universal when gravity-like interaction is present. Our approach to the Dirac equation follows Rund's technique for the algebra of the $γ$-matrices that doesn't rely on the Klein-Gordon equation.

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Vesselin G. Gueorguiev. 2002-10-10. Matter, Fields, and Reparametrization-Invariant Systems. https://arxiv.org/abs/math-ph/0210022

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