Note on an action for a particle in the Ho\v{r}ava-Lifshitz Gravity

TL;DR

This paper revisits a proposed particle action compatible with Hořava-Lifshitz gravity, deriving subluminal and superluminal limits clearly using Hamiltonian methods.

Contribution

It provides a Hamiltonian formulation of the particle action, clarifying the limits without gauge ambiguity in the context of Hořava-Lifshitz gravity.

Findings

Derived subluminal and superluminal particle limits

Clarified gauge-independent Hamiltonian formulation

Enhanced understanding of particle dynamics in Hořava-Lifshitz gravity

Abstract

We reconsider a recently proposed action for a free particle which is compatible with Ho\v{r}ava-Lifshitz gravity, and then obtain the subluminal and the superluminal limits without gauge ambiguity in terms of Hamiltonian formulation.