Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 016, 11 pages      arXiv:0802.0751      http://dx.doi.org/10.3842/SIGMA.2008.016
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time

Roman Ya. Matsyuk
Institute for Applied Problems in Mechanics and Mathematics, 15 Dudayev Str., L'viv, Ukraine

Received October 31, 2007, in final form January 18, 2008; Published online February 06, 2008; Some errors are corrected March 27, 2008

Abstract
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.

Key words: covariant Ostrohrads'kyj mechanics; spin; concircular geometry; uniform acceleration.

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