Hamiltonization of theories with degenerate coordinates

TL;DR

This paper proposes a simplified Hamiltonization method for Lagrangian theories with degenerate coordinates, challenging traditional singularity definitions and avoiding the need to complete degenerate coordinates with conjugate momenta.

Contribution

It introduces a new approach to Hamiltonization for theories with degenerate coordinates, simplifying the process by not requiring conjugate momenta for these coordinates.

Findings

Simplified Hamiltonization procedure for degenerate coordinates

Reconsideration of singularity definition based on Hessian

Avoidance of completing degenerate coordinates with momenta

Abstract

We consider a class of Lagrangian theories where part of the coordinates does not have any time derivatives in the Lagrange function (we call such coordinates degenerate). We advocate that it is reasonable to reconsider the conventional definition of singularity based on the usual Hessian and, moreover, to simplify the conventional Hamiltonization procedure. In particular, in such a procedure, it is not necessary to complete the degenerate coordinates with the corresponding conjugate momenta.