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SIGMA 4 (2008), 016, 11 pages arXiv:0802.0751
https://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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