Phys. Rev. D 60, 044009 (1999) [10 pages]SL(2,R) model with two Hamiltonian constraintsReceived 26 January 1999; published 14 July 1999 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 with 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 classical theory, we solve the equations of motion, find an SO(2,2) algebra of Dirac observables, find the gauge transformations for the Lagrangian and canonical variables and for the Lagrange multipliers. In quantum theory, we find the physical states, the quantum observables, and the physical inner product, which is determined by the reality conditions. In addition, we construct the classical and quantum evolving constants of the system. The model illustrates how to describe physical gauge-invariant relative evolution when coordinate time evolution is a gauge. © 1999 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.60.044009
DOI:
10.1103/PhysRevD.60.044009
PACS:
04.60.Ds
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