Relativistic quantum mechanics of bosons

Egon Marx

Partha Ghose

Partha Ghose, Dipankar Home, M.N. Sinha Roy

Soon-Tae Hong

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.

Sol Wieder

Soon-Tae Hong

Department ofScience Educationand Research Institute forBasicSciences, EwhaWomansUniversity, Seoul 120-750 Korea(Dated: August 15, 2011)We construct a relativistic quantum mechanics for a boson which sustains the positive definiteparticle probability for the relativistic boson. In this theory, we settle down the well-known 85 yearsold unsolved problem on the particle probability of the Klein-Gordon quantum mechanics. Thesolutions for a boson obtained from our theory possess a negative solution as well as a positive one,similar to those of the Dirac quantum mechanics for a fermion. We next study Lorentz transforma-tion, and a vacuum state with all fermion and boson negative energy levels filled and all fermion andboson positive energy levels empty, so that we can have unification of the bosonic sea and the Diracfermionic one. In this unified sea we investigate the bosonic and fermionic antiparticles associatedwith the unified vacuum on an equal footing, and we obtain a charge conjugation operator to studydecay modes of the particles and antiparticles.I. INTRODUTION