Hamiltonian For String in Newton-Cartan Background

TL;DR

This paper develops the Hamiltonian formulation for non-relativistic strings in Newton-Cartan backgrounds, starting from relativistic strings and analyzing the resulting constraints and properties.

Contribution

It introduces a Hamiltonian framework for non-relativistic strings in Newton-Cartan geometry, including constraint analysis and Lagrangian formulation.

Findings

Constraints are first class in the non-relativistic limit.

Derived the Lagrangian for non-relativistic strings.

Established the Hamiltonian structure in Newton-Cartan background.

Abstract

This paper is devoted to the construction of the Hamiltonian for non-relativistic string in the Newton-Cartan background. We start with the Hamiltonian for relativistic string in general background. Then we perform limiting procedure on the metric that leads to Newton-Cartan background. We determine constraint structure for non-relativistic string and show that these constraints are the first class constraints. Then we determine corresponding Lagrangian and discuss its properties.