Nonrelativistic limit of the bosonic string

TL;DR

This paper introduces a new nonrelativistic string action with general covariance, provides its Hamiltonian formulation, and finds specific solutions in the time gauge, expanding the understanding of nonrelativistic string dynamics.

Contribution

It presents the first invariant nonrelativistic string action and its Hamiltonian formulation, along with explicit solutions in a specific gauge.

Findings

Invariant nonrelativistic string action proposed

Hamiltonian formulation derived

Explicit solutions found in the time gauge

Abstract

We propose the action for the nonrelativistic string invariant under general coordinate transformations on the string worldsheet. The Hamiltonian formulation for the nonrelativistic string is given. Particular solutions of the Euler-Lagrange equations are found in the time gauge.