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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 γ-matrices that doesn’t rely on the Klein-Gordon equation.
MSC:
81T30String and superstring theories
81V25Other elementary particle theory
83E15Kaluza-Klein and other higher-dimensional theories
81V17Gravitational interaction