Matter, fields, and reparametrization-invariant systems. (English) Zbl 1023.81035

Gueorguiev, Vesselin

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

Keywords:

higher-dimensional extended object; D-brane; electromagnetism; gravity; integral submanifold embedding; mass-shell constraint; Klein-Gordon equation; Dirac equation; Rund’s technique