Non-canonical Quantization of a Quadratic Constrained System

TL;DR

This paper introduces a non-canonical quantization method for quadratic constrained systems that resolves Jacobi identity issues and produces a well-defined Fock space, aligning with Dirac quantization in non-constrained cases.

Contribution

It presents an alternative quantization approach that addresses key problems in Dirac quantization for quadratic systems, ensuring consistency and a proper Fock space.

Findings

Resolves Jacobi identity violation in quadratic constrained systems

Produces a well-defined Fock space

Aligns with Dirac quantization results for non-constrained systems

Abstract

We propose an alternative to Dirac quantization for a quadratic constrained system. We show that this solves the Jacobi identity violation problem occuring in the Dirac quantization case and yields a well defined Fock space. By requiring the uniqueness of the ground state, we show that for non-constrained systems this approach gives the same results as Dirac quantization.