Geometrical formulation of relativistic mechanics

Autor(es)

Chanda, Sumanto ^[1] ; Guha, Partha ^{[2, 3, 1]}

Afiliação do(s) autor(es)

^[1] Satyendra Nath Bose Natl Ctr Basic Sci, Dept Theoret Sci, JD Block, Sect 3, Kolkata 700098 - India

^[2] Univ Sao Paulo, Inst Fis Sao Carlos, Caixa Postal 369, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Sao Paulo, IFSC USP, Caixa Postal 369, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS; v. 15, n. 4 APR 2018.
• Citações Web of Science: 0

Resumo

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 Lienard oscillator and the spacetime it implies. (AU)

• Processo FAPESP: 16/06560-6 - Dinâmica não-linear e gravidade
• Beneficiário: Betti Hartmann
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional