2017/06/30 by Sumanto Chanda, Partha Guha
Mathematics · Physics and Astronomy · #Covariant transformation #Hamiltonian (control theory) #Invariant (physics) #Lagrangian #Lorentz covariance #Lorentz transformation #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #Relativistic dynamics #Relativistic mechanics #Relativistic particle #Relativity and Gravitational Theory #Spacetime #math-ph #math.MP
paper · pdf · doi:10.1142/s0219887818500627
24 pages
openalex created_date 2017/06/15 · arxiv created 2017/11/24 · openalex publication_date 2017/12/04 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
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.