Introduction to the symplectic group Sp(2)
McKinstrie C.J. Kozlov M.V.
2026Canadian Science Publishing
Canadian Journal of Physics
2026#1041 - 14 pp.
In this article, we derive and discuss the properties of the symplectic group Sp(2), which arises in Hamiltonian dynamics and ray optics. We show that a symplectic matrix can be written as the product of a symmetric dilation matrix and a rotation matrix, in either order. A symplectic matrix can be written as the exponential of a generating matrix, and there is a one-to-one relation between the coefficients of the symplectic and generating matrices. We also discuss the adjoint and Schmidt decompositions of a symplectic matrix, and the product of two symplectic matrices. The results of this article have applications in many subfields of physics.
Hamiltonian dynamics and optics , infinitessimal generators , matrix decompositions , symplectic matrices
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Independent Photonics Consultant, Manalapan, 07726, NJ, United States
Center for Preparatory Studies, Nazarbayev University, Astana, 010000, Kazakhstan
Independent Photonics Consultant
Center for Preparatory Studies
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