The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time
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.
Cite
@article{arxiv.0802.0751,
title = {The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time},
author = {Roman Ya. Matsyuk},
journal= {arXiv preprint arXiv:0802.0751},
year = {2008}
}
Comments
This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ Corrections: Signs in formulae 3.17, 3.18, 3.21, 3.22, next to A.14