Connection Dynamics for Higher Dimensional Scalar-Tensor Theories of Gravity

TL;DR

This paper extends the connection-dynamical formalism and Hamiltonian analysis of scalar-tensor theories of gravity to higher dimensions, revealing their similarity to 4D cases and enabling loop quantum gravity techniques.

Contribution

It provides a Hamiltonian framework for higher-dimensional scalar-tensor theories, showing their connection to Yang-Mills structures and facilitating non-perturbative quantization methods.

Findings

Hamiltonian analysis of higher-dimensional scalar-tensor theories

Identification of a symplectic reduction linking Yang-Mills and scalar-tensor structures

Applicability of loop quantum gravity techniques to higher-dimensional theories

Abstract

The scalar-tensor theories of gravity in spacetime dimensions $D+1>2$ are studied. By doing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the theories are naturally divided into two sectors by the coupling parameter $\omega$. The Hamiltonian structure in both sectors are similar to the corresponding structure of 4-dimensional cases. It turns out that there is a symplectic reduction from the canonical structure of $so(D+1)$ Yang-Mills theories coupled to the scalar field to the canonical structure of the geometrical scalar-tensor theories. Therefore the non-perturbative loop quantum gravity techniques can also be applied to the scalar-tensor theories in $D+1$ dimensions based on their connection-dynamical formalism.