6533b836fe1ef96bd12a01a3

RESEARCH PRODUCT

Covariant phase-space quantization of the induced 2D gravity

Victor AldayaVictor AldayaJosé Navarro-salasMiguel Navarro

subject

PhysicsNuclear and High Energy PhysicsPure mathematicsCanonical quantizationHilbert spaceCotangent spacesymbols.namesakeConjugacy classOperator algebraQuantum mechanicsPhase spacesymbolsCovariant transformationConfiguration spaceGeneral Theoretical Physics

description

Abstract We study in a parallel way the induced 2D gravity and the Jackiw-Teitelboimmodel on the cylinder from the viewpoint of the covariant description of canonical formalism. We compute explicity thhe symplectic structure of both theories showing that their (reduced) phase spaces are finite-dimensional cotangent bundles. For the Jackiw-Teitelboim model the base space (configuration space) is the space of conjugacy classes of the PSL(2, R ) group. For the induced 2D gravity, and Λ > 0, the (reduced) phase space consist of two (identical) connected components each one isomorphic to the contangent bundle of the space of hyperbolic conjugacy classes of the PSL (2, R ) group, whereas for Λ R ). This result permits the physical Hilbert space both theories to be determined exactly.

https://doi.org/10.1016/0550-3213(93)90037-p