On the Hilbert space dimension of systems with second class constraints

TL;DR

This paper demonstrates that quantized dynamical systems with second class constraints inherently possess an infinite-dimensional Hilbert space, highlighting a fundamental property of such constrained quantum systems.

Contribution

The work establishes a general proof that systems with second class constraints always lead to infinite-dimensional Hilbert spaces upon quantization.

Findings

Quantized systems with second class constraints have infinite-dimensional Hilbert spaces.

The result applies broadly to constrained quantum systems.

Provides insight into the structure of constrained quantum theories.

Abstract

It is shown that quantized dynamical system with second class constraints has infinite dimensional Hilbert space.