The Klein-Gordon-Fock theory as a one-particle relativistic quantum mechanics

Abstract:The Klein-Gordon-Fock (KGF) theory with scalar and vector potentials is presented as a one particle relativistic quantum mechanics (QM). First, the KGF equation is written in a Hamiltonian form, in spinor space; unlike the Feshbach-Villars approach, the Hamiltonian here is strictly Hermitian. Then this equation is rewritten for a one-component wave function. Expressions for the Hamiltonian and other observables' operators acting in the space of one-component wave functions are presented. The nonrelativistic and ultrarelativistic limits of these expressions are considered. A general solution to the KGF equation describing a free particle is presented.

arXiv:2607.26431 [quant-ph]

(or arXiv:2607.26431v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.26431 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.