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

• URL: http://arxiv.org/abs/2607.26431v1
• Date: Wed, 29 Jul 2026 03:17:46 GMT
• Title: The Klein-Gordon-Fock theory as a one-particle relativistic quantum mechanics
• Abstract summary: The Klein-Gordon-Fock (KGF) theory with scalar and vector potentials is presented as a one particle relativistic quantum mechanics (QM)<n>The KGF equation is written in a Hamiltonian form, in spinor space; unlike the Feshbach-Villars approach, the Hamiltonian here is strictly Hermitian.<n>A general solution to the KGF equation describing a free particle is presented.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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