Canonical Commutation Relation Derived from Witt Algebra

From an abstract definition of operators inspired on the oscillators of Virasoro, an algebra is derived. It encompasses the structure of Virasoro with null charge central or Witt algebra. The applied formalism has yielded commutators with a dependence on integer numbers, and it follows a kind of Witt-like algebra. Indeed, the quantum mechanics evolution operator for the case of quantum harmonic oscillator was identified. Also, Schrödinger equation was systematically derived, inside the present framework. When operators are expressed in the framework of Hilbert space states, the resulting Witt-like algebra seems to be proportional to well-known canonical commutation relation. This has demanded to develop a formalism based on abstract and physical operators as well as well-defined rules of commutation. The Witt-like was also redefined through the direct usage of uncertainty principle. It might to be suggesting that Witt algebra encloses not only quantummechanicsfundamentalcommutator, butalsodifferent relations among quantummechanics observables.