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Geometrical formulation of relativistic mechanics

Department of Theoretical Sciences, Satyendra Nath Bose National Centre for Basic Sciences, JD Block, Sector-3, Salt Lake, Kolkata 700098, India

E-mail Address: sumanto12@bose.res.in

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and

Partha Guha

Department of Theoretical Sciences, Satyendra Nath Bose National Centre for Basic Sciences, JD Block, Sector-3, Salt Lake, Kolkata 700098, India

Instituto de Física de São Carlos; IFSC/USP, Universidade de São Paulo Caixa Postal 369, CEP 13560-970, São Carlos-SP, Brazil

E-mail Address: partha@bose.res.in

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https://doi.org/10.1142/S0219887818500627Cited by:10 (Source: Crossref)

Abstract

The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler–Lagrange equation, and relativistic Hamiltonian mechanics. We also formulate a modified local Lorentz transformation, such that the metric at a point is invariant only under the transformation defined at that point, and derive the formulae for time-dilation, length contraction, and gravitational redshift. Then we compare our formulation under non-relativistic approximations to the conventional ad hoc formulation, and we briefly analyze the relativistic Liénard oscillator and the spacetime it implies.

Keywords:

AMSC: 83A05, 83D05

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