Semiclassical States for Constrained Systems

TL;DR

This paper refines the concept of semi-classical states for constrained systems, applying group averaging to kinematical coherent states, and demonstrates the effectiveness of this approach in specific examples.

Contribution

It clarifies semi-classical states for constrained systems and introduces an efficient method using group averaging on kinematical states.

Findings

Group averaging effectively produces physical semi-classical states.

The technique is surprisingly efficient in specific examples.

Kinematical structures can analyze semi-classical behavior of constrained systems.

Abstract

The notion of semi-classical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is applied to kinematical coherent states to obtain physical semi-classical states. In the specific examples considered, the technique turns out to be surprisingly efficient, suggesting that it may well be possible to use kinematical structures to analyze the semi-classical behavior of physical states of an interesting class of constrained systems.