On The Quantization Of Constraint Systems: A Lagrangian Approach

TL;DR

This paper explores a Lagrangian approach to quantizing constraint systems with singular Lagrangians, introducing a generalized Gupta-Bleuler method that yields true Schrödinger equations in specific examples.

Contribution

It proposes a novel quantization method for systems with singular Lagrangians using a Lagrangian framework and generalized Gupta-Bleuler quantization.

Findings

The method produces valid Schrödinger equations in example systems.

It extends quantization techniques to systems with external background fields.

The approach handles constraints in a Lagrangian formalism.

Abstract

It is possible to introduce external time dependent back ground fields in the formulation of a system as fields whose dynamics can not be deduced from Euler Lagrange equations of motion. This method leads to singular Lagrangians for real systems. We discuss quantization of constraint systems in these cases and introduce generalized Gupta-Bleuler quantization. In two examples we show explicitly that this method of quantization leads to true Schr\"{o}dinger equations.