On Hamiltonian approach on 3+1-dimensional space-time

TL;DR

This paper introduces a 4D Hamiltonian framework for Minkowski space-time applicable to both quantum and classical, relativistic and non-relativistic physics, aiming to unify and extend Hamiltonian mechanics.

Contribution

It presents a novel 4-dimensional Hamiltonian formulation tailored for Minkowski space-time, bridging classical and quantum, relativistic and non-relativistic theories.

Findings

Unified Hamiltonian approach for different physical regimes

Applicable to both quantum and classical systems

Extends Hamiltonian mechanics to 4D space-time

Abstract

The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic problems.