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Matter, fields, and reparametrization-invariant systems. (English) Zbl 1023.81035
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 4th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 6-15, 2002. Sofia: Coral Press Scientific Publishing. 168-177 (2003).
Summary: 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.
For the entire collection see [Zbl 1008.00022].
##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81V25 Other elementary particle theory in quantum theory 83E15 Kaluza-Klein and other higher-dimensional theories 81V17 Gravitational interaction in quantum theory
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