Akintsov, N.S.; Nevecheria, A.P.; Kopytov, G.F.; Yang, Y.; Cao, T. Special Relativity in Terms of Hyperbolic Functions with Coupled Parameters in 3+1 Dimensions. Symmetry2024, 16, 357.
Akintsov, N.S.; Nevecheria, A.P.; Kopytov, G.F.; Yang, Y.; Cao, T. Special Relativity in Terms of Hyperbolic Functions with Coupled Parameters in 3+1 Dimensions. Symmetry 2024, 16, 357.
Akintsov, N.S.; Nevecheria, A.P.; Kopytov, G.F.; Yang, Y.; Cao, T. Special Relativity in Terms of Hyperbolic Functions with Coupled Parameters in 3+1 Dimensions. Symmetry2024, 16, 357.
Akintsov, N.S.; Nevecheria, A.P.; Kopytov, G.F.; Yang, Y.; Cao, T. Special Relativity in Terms of Hyperbolic Functions with Coupled Parameters in 3+1 Dimensions. Symmetry 2024, 16, 357.
Abstract
This paper presents a new method for parameterizing the Lorentz group based on coupled parameters. From the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra in terms of elementary functions when explicit decomposition is difficult. New rapidity-dependent Lorentz-invariant coordinates are obtained, and the descriptions of particle motion using the old and new Lorentz-invariant forms as applied to plane waves are compared. Based on a classical model of particle motion in the field of a plane monochromatic electromagnetic wave and in that of a plane laser pulse, the rapidity-dependent spectral decompositions into elementary functions are presented, and the Euler–Hamilton equations are derived as rapidity functions in 3+1 dimensions.
Keywords
new Lorentz-invariant coordinates; angular and perpendicular rapidities; Gudermann function; passage to the limit; Euler-Hamilton equation; Euler-Lagrange equations
Subject
Physical Sciences, Theoretical Physics
Copyright:
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