Solution of Constraints in Theory of Relativistic String

TL;DR

This paper develops a Hamiltonian framework for relativistic string theory using diffeomorphism-invariant variables, enabling the explicit solution of energy constraints and Hamiltonian reduction.

Contribution

It introduces a method to solve energy constraints in the Hamiltonian formulation of relativistic strings using diffeomorphism-invariant variables.

Findings

Constructed energy invariant with respect to time-coordinate transformations

Solved the energy constraint explicitly

Performed Dirac's Hamiltonian reduction

Abstract

The Hamiltonian theory of a relativistic string is considered in a specific reference frame in terms the diffeo-invariant variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Noether theorem. This coincidence allows us to solve the energy constraint, and fulfil Dirac's Hamiltonian reduction.