The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time

TL;DR

This paper develops a variational principle for geodesic circles in two-dimensional (pseudo)-Riemannian space, linking it to uniform acceleration and spin-curvature interactions in relativistic particles.

Contribution

It introduces a new variational framework for geodesic circles in 2D space-time, connecting geometric invariants with physical notions of acceleration and spin.

Findings

Derivation of the variational principle for geodesic circles

Identification of spin-curvature interaction from second derivatives

Reduction to invariant equations of constant Frenet curvature

Abstract

The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.