Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action

TL;DR

This paper applies the Hamiltonian GNH analysis to a parametrized unimodular extension of the Holst action, providing a clear geometric Hamiltonian formulation and explaining the challenges in other methods.

Contribution

It offers a detailed GNH-based Hamiltonian analysis of the unimodular Holst extension, clarifying the geometric structure and constraints involved.

Findings

Derived a simple Hamiltonian formulation for the model

Identified the geometric nature of the constraints

Explained the difficulty of other approaches

Abstract

We give a detailed account of the Hamiltonian GNH analysis of the parametrized unimodular extension of the Holst action. The purpose of the paper is to derive, through the clear geometric picture furnished by the GNH method, a simple Hamiltonian formulation for this model and explain why it is difficult to arrive at it in other approaches. We will also show how to take advantage of the field equations to anticipate the simple form of the constraints that we find in the paper.