How is Lorentz Invariance encoded in the Hamiltonian?

TL;DR

This paper presents a method to directly verify Lorentz invariance from the Hamiltonian for certain theories, simplifying the process of checking relativistic consistency without solving equations of motion or computing Poisson brackets.

Contribution

It introduces a novel approach to determine Lorentz invariance directly from the Hamiltonian for a specific class of theories.

Findings

Method allows direct Lorentz invariance check from Hamiltonian

Applicable to theories where traditional methods are difficult

Simplifies the verification process for relativistic invariance

Abstract

One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson Brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.