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VOL. 4 | 2003 Matter, Fields, and Reparametrization-Invariant Systems
Vesselin Gueorguiev

Editor(s) Ivaïlo M. Mladenov, Gregory L. Naber

## 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 $\gamma$-matrices that doesn’t rely on the Klein–Gordon equation.

## Information

Published: 1 January 2003
First available in Project Euclid: 12 June 2015

zbMATH: 1023.81035
MathSciNet: MR1977566

Digital Object Identifier: 10.7546/giq-4-2003-168-177