An SL(2,R) model of constrained systems with two hamiltonian constraints
Abstract
We describe a simple dynamical model characterized by the presence of two noncommuting hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one hamiltonian constraint associated to each space point. We solve the classical and quantum dynamics of the model, which turns out to be governed by an SL(2,R) gauge symmetry, local in time. In the classical theory, we solve the equations of motion, find a SO(2,2) algebra of Dirac observables, find the gauge transformation for the lagrangian and canonical variables and for the Lagrange multipliers. In the quantum theory, we find physical states and quantum observables. In addition, we construct the classical and quantum evolving constants of the system.Keywords
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