Time reparametrization-invariant dynamics of a relativistic string

TL;DR

This paper develops a reparametrization-invariant Hamiltonian formulation for a relativistic string, identifying a proper time parameter and simplifying the dynamics through canonical transformations, advancing the theoretical understanding of string evolution.

Contribution

It introduces a method to resolve constraints in the string's Hamiltonian framework, defining a proper time and reducing the system to an unconstrained form using canonical transformations.

Findings

Derived a reparametrization-invariant Hamiltonian for the string.

Identified the string's center of mass time with proper time.

Reduced the constrained system to an unconstrained form with a Roehrlich-type Hamiltonian.

Abstract

The time-reparametrization-invariant dynamics of a relativistic string is studied in the Dirac generalized Hamiltonian theory by resolving the first class constraints. The reparametrization-invariant evolution parameter is identified with the time-like coordinate of the "center of mass" of a string which is separated from local degrees of freedom by transformations conserving the group of diffeomorphisms of the generalized Hamiltonian formulation and the Poincare covariance of local constraints. To identify the "center of mass" time-like coordinate with the invariant proper time (measured by an observer in the comoving frame of reference), we apply the Levi-Civita - Shanmugadhasan canonical transformations which convert the global (mass-shell) constraint into a new momentum, so that the corresponding gauge is not needed for the Hamiltonian reduction. The resolving of local constraints leads to an "equivalent unconstrained system" in the reduced phase space with the Roehrlich-type Hamiltonian of evolution with respect to the proper time.