Formal power series, operator calculus, and duality on Lie algebras

摘要: This paper presents an operator calculus approach to computing with non-commutative variables. First, we recall the product formulation of formal exponential series. Then show how formulate canonical boson on is used represent action a Lie algebra its universal enveloping algebra. As applications, Hamilton's equations for general Hamiltonian, given as series, are found using double-dual representation, and adjoint representation given. With these techniques one can Volterra acting We illustrate three-step nilpotent