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GR: Gravitation und Relativitätstheorie

GR 3: Post-Einsteinsche Modelle

GR 3.4: Vortrag

Dienstag, 24. März 1998, 17:30–17:50, H47

Spaces with torsion from embedding and the special role of autoparallel trajectories — •S.V. Shabanov and H. Kleinert — Institute for Theoretical Physics, FU-Berlin, Arnimallee 14, WE 2, D-14195, Berlin, Germany

As a contribution to the ongoing discussion of trajectories of spinless particles in spaces with torsion we show that the geometry of such spaces can be induced by embedding their curves in a higher-dimensional euclidean space without torsion. Technically speaking, we define the tangent (velocity) space of the embedded space imposing non-holonomic constraints (see, e.g. [1]) upon the tangent space of the embedding space. Parallel transport in the embedded space is determined as an induced parallel transport on the surface of constraints. Gauss’ principle [1] of least constraint is used to show that autoparallels realize a constrained motion that has a minimal deviation from the free, unconstrained motion, this being a mathematical expression of the principle of inertia. In contrast, geodesics play no special role in the constrained dynamics, making them less likely candidates for particle trajectories [2].

[1] L.A. Pars, A Treatise on Analytical Dynamics (Heinemann, London, 1965)

[2] H. Kleinert, S.V. Shabanov, FU-Berlin preprint, September, 1997; gr-cq/9709067