Simplicial Euclidean Relativistic Lagrangian

1994/07/13 by Marius I. Piso, Piso, Marius. I.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.gr-qc/9407015

openalex publication_date 1994/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paths on the \bf R³ real Euclidean manifold are defined as 2-dimensional simplicial strips; points are replaced by 2-simplexes and the orbits of the action of a one discrete-parameter group on the base manifold becomes a convex polyhedron attached to a 2-dimensional simplicial complex. The Lagrangian of a moving mass is proportional to the width of the path. The special relativistic form of the Lagrangian is recovered in the continuum limit, without relativistic Lorenz invariance considerations.

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