Poincar\'e generators at second post-Minkowskian order

TL;DR

This paper confirms the Poincaré invariance of the Hamiltonian formulation of binary gravitating systems at the second post-Minkowskian order, providing a general Hamiltonian and boost generator consistent with the Poincaré algebra.

Contribution

It derives the 2PM Hamiltonian in an arbitrary frame and constructs the corresponding boost generator, extending previous results to a more general setting.

Findings

Verified Poincaré invariance at 2PM order

Derived a general 2PM Hamiltonian in any reference frame

Constructed the 2PM boost generator satisfying Poincaré algebra

Abstract

We verify the global Poincar\'e invariance of the Hamiltonian mechanics of gravitating binary dynamics at the second post Minkowskian (2PM) order. For spinless point particles, based on the known 2PM Hamiltonian in the center of momentum frame, we compute the general 2PM Hamiltonian valid in an arbitrary reference frame. An off-shell extension of the 1PM Hamiltonian, which contributes at the 2PM order through an iteration process, plays a crucial role. We then construct the 2PM boost generator that uniquely satisfies all the conditions imposed by the Poincar\'e algebra.