A novel realization of the Virasoro algebra in number state space

The group of diffeomorphisms is crucial in quantum computing. Representing it by vector fields over a d  -manifold, d⩾2d⩾2, accounting for both projective action and conformal symmetry at the quantum mechanical level, requires the direct-sum decomposition of tensor product for non-compact algebras, viable only for su(1,1)su(1,1). As a step towards the solution, a realization of the (d=1d=1) Virasoro algebra Vir∼Diff+(S(1))Vir∼Diff+(S(1)) in the universal envelope of su(1,1)su(1,1) (and h(1)h(1)) is presented, which is simple in the discrete positive series irreducible unitary representation Dκ(+) of su(1,1)su(1,1).