A new Hamiltonian for a massive relativistic particle with spin one in a generalized Heisenberg/Schr\"odinger picture

TL;DR

This paper introduces a novel Hamiltonian for a massive relativistic particle with spin one, derived through a generalized transformation between Heisenberg and Schrödinger pictures using Lorentz group representations.

Contribution

It presents a new Hamiltonian operator for spin-one particles based on a 4D generalization of the Heisenberg/Schrödinger transition employing Lorentz group representations.

Findings

Derived a new Hamiltonian for spin-one particles.

Applied Fourier transformation in a generalized Heisenberg/Schrödinger framework.

Extended the transition between pictures to a 4D Lorentz-invariant setting.

Abstract

We consider a particular 4-dimensional generalization of the transition from the Heisenberg to the Schr\"odinger picture. The space-time independent expansion with respect to the unitary irreducible representations of the Lorentz group is applied, as Fourier transformation in the Heisenberg picture, to the states of a massive relativistic particle. A new Hamiltonian operator has been found for such a particle with spin one.