Geometry and Dynamics with Time-Dependent Constraints

TL;DR

This paper develops geometrical methods to handle systems with explicit time-dependent constraints, enabling Hamiltonian formulation and gauge fixing for complex physical systems like relativistic particles and strings.

Contribution

It introduces a geometric approach to incorporate time-dependent second-class constraints into Hamiltonian systems, facilitating gauge fixing in relativistic models.

Findings

Hamiltonian form on physical phase space achieved

Gauge fixing of relativistic particles demonstrated

Application to strings in electromagnetic backgrounds

Abstract

We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which require time-dependent gauge fixing conditions in order to reduce them to their physical degrees of freedom. To illustrate our results we discuss the gauge-fixing of relativistic particles and strings moving in arbitrary background electromagnetic and antisymmetric tensor fields.