On representations of the canonical commutation relations by time and energy operators

Abstract

We give a survey of recent results in the representation theory of the Heisenberg Lie Algebra by time and energy operators. This representation is non standard and hence distinct from the Schrodinger representation. They deserve attention from mathematicians because they arise in the consideration of concrete problems in physics regarding the nature of time in quantum mechanics.  Representations in the space of deformed algebras via supraquantization is another point of interest for the time-energy commutation relations.