Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity

TL;DR

This paper addresses the multivalued Hamiltonian issue in Lanczos-Lovelock gravity by proposing an extended theory that ensures a unique Hamiltonian, facilitating manifest diffeomorphic invariance and canonical quantization.

Contribution

The authors introduce an extended Lanczos-Lovelock gravity theory that resolves the branched Hamiltonian problem, enabling a consistent Hamiltonian formulation and quantization.

Findings

Constructed a unique Hamiltonian in the extended theory.

Achieved manifest diffeomorphic invariance.

Facilitated canonical quantization of the model.

Abstract

The Hamiltonian constraint Hc = NH = 0, defines a diffeomorphic structure on spatial manifolds by the lapse function N in general theory of relativity. However, it is not manifest in Lanczos-Lovelock gravity, since the expression for velocity in terms of the momentum is multivalued. Thus the Hamiltonian is a branch function of momentum. Here we propose an extended theory of Lanczos-Lovelock gravity to construct a unique Hamiltonian in its minisuperspace version, which results in manifest diffeomorphic invariance and canonical quantization.