A canonical formalism of f(T)-type gravity in terms of Lie derivatives

TL;DR

This paper develops a canonical formalism for f(T)-type gravity using Lie derivatives, addressing and resolving issues present in previous formalisms like Buchbinder and Lyakhovich's approach.

Contribution

It introduces a new canonical formalism for f(T)-type gravity based on Lie derivatives, improving upon prior methods such as BL.

Findings

Successfully resolves the formalism problem in BL approach.

Defines conjugate momenta and Hamiltonian density using Lie derivatives.

Provides a consistent canonical framework for f(T)-type gravity.

Abstract

A canonical formalism of f(R)-type gravity is proposed, resolving the problem in the formalism of Buchbinder and Lyakhovich(BL). The new coordinates corresponding to the time derivatives of the metric are taken to be its Lie derivatives which is the same as in BL. The momenta canonically conjugate to them and Hamiltonian density are defined similarly to the formalism of Ostrogradski. It is shown that our method surely resolves the problem of BL.