Particles and Strings in Degenerate Metric Spaces

TL;DR

This paper explores the dynamics of particles and strings in degenerate metric spaces, classifies the resulting constraints, and initiates quantization methods for non-relativistic particles.

Contribution

It provides a detailed classification of constraints and links null eigenvectors to Killing vectors in degenerate metrics, advancing understanding of such systems.

Findings

Constraints depend on the parity of space dimension and metric rank

Null eigenvectors correspond to Killing vectors in certain degenerate metrics

First steps towards quantization of non-relativistic particles in these spaces

Abstract

We consider relativistic and non-relativistic particles and strings in spaces (or space-times) with a degenerate metric. We show that the resulting dynamics is described by a rich structure of constraints. All constraints are classified and the dynamics depends strongly on the parity of the difference between the dimension of the space (or space-time) and the rank of the degenerate metric. For a particular class of degenerate metrics we can identify the null eigenvectors of the metric with its Killing vectors. We also give the first steps towards the quantization of the non-relativistic particle using the Senjanovic path integral quantization and the Batalin-Fradkin-Tyutin conversion method.