Symmetries of space-time

TL;DR

This paper explores the fundamental differences and implications of Hamiltonian and Lagrangian formulations of gravity, emphasizing their distinct perspectives on space-time symmetries and recent mathematical developments.

Contribution

It provides a comparative analysis of Hamiltonian and Lagrangian gravity, highlighting their unique insights into space-time symmetries and recent mathematical support.

Findings

Hamiltonian gravity equations are less elegant but fundamental.

Both formulations reveal different aspects of space-time symmetries.

Recent mathematical tools support the understanding of these formulations.

Abstract

The equations of Hamiltonian gravity are often considered ugly cousins of the elegant and manifestly covariant versions found in the Lagrangian theory. However, both formulations are fundamental in their own rights because they make different statements about the nature of space-time and its symmetries. These implications, along with the history of their derivation and an introduction of recent mathematical support, are discussed here.