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arXiv · 1902.05913

$Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry

E. Choreño·D. Ojeda-Guillén
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Abstract

In this paper we introduce the bosonic generators of the $sp(4,R)$ algebra and study some of their properties, based on the $SU(1,1)$ and $SU(2)$ group theory. With the developed theory of the $Sp(4,R)$ group, we solve the interaction part of the most general Hamiltonian of a two-level system in two-dimensional geometry in an exact way. As particular cases of this Hamiltonian, we reproduce the solution of earlier problems as the Dirac oscillator and the Jaynes-Cummings model with one and two modes of oscillation.

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E. Choreño, D. Ojeda-Guillén. 2019-02-15. $Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry. https://doi.org/10.1140/epjp/i2019-12962-9

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