1. Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach
- Author
-
Alejandro Kunold, J. C. Sandoval-Santana, V. G. Ibarra-Sierra, and J. L. Cardoso
- Subjects
Adjoint representation ,FOS: Physical sciences ,Real form ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,01 natural sciences ,Affine Lie algebra ,Representation theory ,010305 fluids & plasmas ,Graded Lie algebra ,Lie conformal algebra ,Algebra ,0103 physical sciences ,Lie bracket of vector fields ,010306 general physics ,Mathematical Physics ,Heisenberg picture ,Mathematics ,Mathematical physics - Abstract
We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to uniform and constant electro-magnetic fields., Comment: 17 pages, 3 tables
- Published
- 2016
- Full Text
- View/download PDF