Group of Transformations with Respect to the Counterpart of Rapidity and Related Field Equations

DOI

10.1142/S1402925112500349How to use a DOI?

Keywords

Relativistic dynamics; inertial mass; rapidity; co-rapidity; energy-momentum; Lorentz-group; electromagnetic field; notoph field

Abstract

The Lorentz-group of transformations usually consists of linear transformations of the coordinates, keeping as invariant the norm of the four-vector in (Minkowski) space-time. Besides those linear transformations, one may construct different forms of nonlinear transformations of the coordinates keeping unchanged that respective invariant. In this paper we explore nonlinear transformations of second-order which have a natural interpretation within the framework of Yamaleev's concept of the counterpart of rapidity (co-rapidity). The purpose of developed concept is to show that the formulae for energy and momentum of the relativistic particle become regular near the zero-mass and speed of light states. Furthermore, in a covariant formulation, the co-rapidity is presented as a four-vector which admits an extension of the Lorentz-group of transformations. In this paper we additionally show, that in the same way as the rapidity is related to the electromagnetic field, the co-rapidity is related to the field of strengths, which are given by a four-vector. The corresponding equations of such a field are also constructed.

Copyright

© 2012 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Adán R. Rodríguez-Domínguez
AU  - Alejandro Martínez-González
PY  - 2012
DA  - 2012/12/31
TI  - Group of Transformations with Respect to the Counterpart of Rapidity and Related Field Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 580
EP  - 594
VL  - 19
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500349
DO  - 10.1142/S1402925112500349
ID  - Rodríguez-Domínguez2012
ER  -