The relativistic mechanics in a nonholonomic setting : a unified approach to particles with non-zero mass and massless particles
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Physics A: Mathematical and Theoretical |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1088/1751-8113/45/25/255202 |
| Field | Theoretical physics |
| Keywords | Lagrangian; nonholonomic constraint; reduced Chetaev equations; constraint force;Lorentz force; Dicke force; tachyons; particles with zero mass |
| Description | A new approach to relativistic mechanics is proposed, suitable to describe in a unified way dynamics of different kinds of relativistic particles. Mathematically it is an application of a geometric theory of nonholonomic systems on fibred manifolds. We propose a setting based on a naturally constructed Lagrangian and a constraint on the four-velocity of a particle that allows a unified approach to particles with any (positive/negative/zero) square of mass. The corresponding equations of motion are obtained and discussed. In particular, new forces are found (different from the usual Lorentz force type term), arising due to the nonholonomic constraint. A possible meaning and relation with forces previously proposed by Dicke is discussed. In particular, equations of motion of massless particles and of tachyons are studied and the corresponding dynamics are investigated. |
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