Super Finsler Connection of Superparticle on Two Dimensional Curved Spacetime

TL;DR

This paper models a superparticle on a 2D curved spacetime using super Finsler geometry, introducing a nonlinear connection that preserves the metric and reformulates the equations of motion as auto-parallel equations.

Contribution

It proposes a super Finsler connection for superparticles on curved spacetime and explicitly computes this connection, providing a geometric framework for their equations of motion.

Findings

Defined a super Finsler metric on a supermanifold.

Constructed a nonlinear Finsler connection preserving the metric.

Reformulated superparticle equations as auto-parallel equations.

Abstract

We analyze the Casalbuoni-Brink-Schwarz superparticle model on a 2-dimensional curved spacetime as a super Finsler metric defined on a (2,2)-dimensional supermanifold. We propose a nonlinear Finsler connection which preserves this Finsler metric and calculates it explicitly. The equations of motion of the superparticle are reconstructed in the form of auto-parallel equations expressed by the super nonlinear connection.