Faddeev-Jackiw Quantization of Non-Autonomous Singular Systems

TL;DR

This paper extends the Faddeev-Jackiw quantization method to non-autonomous singular systems, resulting in a generalized Schrödinger equation and demonstrating its application on damped harmonic oscillators and relativistic particles.

Contribution

It introduces a novel extension of the Faddeev-Jackiw quantization approach to non-autonomous systems, broadening its applicability.

Findings

Generalized Schrödinger equation for non-autonomous systems

Successful quantization of damped harmonic oscillator

Quantization of relativistic particle in external field

Abstract

We extend the quantization \`a la Faddeev-Jackiw for non-autonomous singular systems. This leads to a generalization of the Schr\"odinger equation for those systems. The method is exemplified by the quantization of the damped harmonic oscillator and the relativistic particle in an external electromagnetic field.