Quantum mechanics for relativistic bosons

TL;DR

This paper develops a relativistic quantum mechanics framework for bosons using two-component wave functions, addressing issues in Klein-Gordon theory and providing a consistent Hamiltonian formulation.

Contribution

It introduces a novel formalism for relativistic bosons with a fixed probability density issue and a diagonal Hamiltonian, expanding quantum mechanics for bosonic particles.

Findings

Successfully constructs a two-component wave function formalism

Resolves probability density issues in Klein-Gordon theory

Provides a diagonal Hamiltonian for relativistic bosons

Abstract

We construct a relativistic quantum mechanics for a boson. To do this we exploit two component wave functions in Dirac type equations of motion. In our formalism we fix the pathological aspect of particle probability density which appears in Klein-Gordon theory. Our solutions possess a negative solution as well as a positive one. We also formulate a diagonal Hamiltonian of the relativistic quantum mechanics for the boson.