Generators of Local Lorentz Transformation in ADM-Vielbein Formalism of Gravitational Relativity

TL;DR

This paper derives the explicit form of the constraints generating local Lorentz transformations in the ADM-Vielbein formalism of general relativity, clarifying their algebraic structure.

Contribution

It provides the complete form of the first class constraints that generate local Lorentz symmetry in the Hamiltonian ADM-Vielbein formalism.

Findings

Constraints obey the Lorentz algebra

Explicit form of Lorentz generators derived

Clarifies gauge symmetry structure in formalism

Abstract

General relativity contains 16 variables in the framework of ADM-Vielbein formalism which are 6 more than metric formalism. These variables emerge due to additional symmetry of Local Lorentz Transformations. In the framework of the Hamiltonian approach, it is expected to find first class constraints which generate this gauge symmetry. We introduce the complete form of such constraints and show that they exactly obey the algebra of the Lorentz group.