Comments on Hamiltonian formalism of AdS/CFT correspondence

As a toy model to search for Hamiltonian formalism of the AdS/CFT correspon dence, we examine a Hamiltonian formulation of the AdS(2)/CFT1 corresponden ce emphasizing unitary representation theory of the symmetry. In the course of a canonical quantization of the bulk scalars, a particular isomorphism between the unitary irreducible representations in the bulk and boundary th eories is found. This isomorphism defines the correspondence of field opera tors. It states that field operators of the bulk theory are field operators of the boundary theory by taking their boundary values in a specific way. The Euclidean continuation provides an operator formulation on the hyperbol ic coordinates system. The associated Fock vacuum of the bulk theory is loc ated at the boundary, thereby identified with the boundary CFT vacuum. The correspondence is interpreted as a simple mapping of the held operators act ing on this unique vacuum. Generalization to higher dimensions is speculate d.