Quantization of soluble classical constrained systems

TL;DR

This paper introduces a novel method for deriving classical brackets in constrained systems without using Dirac's or Faddeev-Jackiw's formalism, simplifying the quantization process.

Contribution

A new approach based on brackets between integration constants of exact solutions, avoiding traditional formalisms for classical constrained systems.

Findings

Simplifies the derivation of classical brackets.

Provides a straightforward way to obtain all brackets from exact solutions.

Facilitates the quantization of constrained systems.

Abstract

The derivation of the brackets among coordinates and momenta for classical constrained systems is a necessary step toward their quantization. Here we present a new approach for the determination of the classical brackets which does neither require Dirac's formalism nor the symplectic method of Faddeev and Jackiw. This approach is based on the computation of the brackets between the constants of integration of the exact solutions of the equations of motion. From them all brackets of the dynamical variables of the system can be deduced in a straightforward way.