# Eisenhart lift and Randers-Finsler formulation for scalar field theory

## TL;DR

This paper extends Eisenhart lifts and Randers-Finsler formulations from point particle mechanics to scalar field theories and Nambu-Goto actions, providing new geometric insights into these theories.

## Contribution

It introduces a novel extension of Eisenhart lifts and Randers-Finsler formulations to scalar field and string actions, broadening their applicability.

## Key findings

- Extended Eisenhart lift to scalar field theory.
- Developed Randers-Finsler formulation for Nambu-Goto action.
- Provided a Jacobi Lagrangian for string actions.

## Abstract

We study scalar field theory as a generalization of point particle mechanics using the Polyakov action, and demonstrate how to extend Lorentzian and Riemannian Eisenhart lifts to the theory in a similar manner. Then we explore extension of the Randers-Finsler formulation and its principles to the Nambu-Goto action, and describe a Jacobi Lagrangian for it.