Relativistic and Newton-Cartan Particle in de Broglie-Bohm Theory

TL;DR

This paper explores the behavior of massive particles in relativistic and Newton-Cartan backgrounds within de Broglie-Bohm theory, deriving Hamilton-Jacobi equations and analyzing classical versus quantum descriptions.

Contribution

It introduces classical and quantum Hamilton-Jacobi equations in these backgrounds and clarifies their fundamental differences within de Broglie-Bohm theory.

Findings

Derived classical and quantum Hamilton-Jacobi equations.

Established relations between Hamilton-Jacobi and wave equations.

Highlighted fundamental differences between classical and quantum systems.

Abstract

This paper is devoted to the analysis of massive particle in general and Newton-Cartan Background in de Broglie-Bohm Theory. We find classical and quantum version of Hamilton-Jacobi equations and find their relations to wave equations. We also discuss fundamental difference between classical and quantum description of these two systems.