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Simplicial Euclidean Relativistic Lagrangian

Marius. I. Piso
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Abstract

The paths on the {\bf R$^3$} 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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Marius. I. Piso. 2003-01-13. Simplicial Euclidean Relativistic Lagrangian. https://arxiv.org/abs/gr-qc/9407015

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