# SL(2,R) model with two Hamiltonian constraints

Montesinos M, Rovelli C, Thiemann T (1999)

**Publication Status:** Published

**Publication Type:** Journal article

**Publication year:** 1999

### Journal

**Publisher:** AMER PHYSICAL SOC

**Book Volume:** 60

**Journal Issue:** 4

### 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 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. [S0556-2821(99)02014-7].

### Authors with CRIS profile

### How to cite

**APA:**

Montesinos, M., Rovelli, C., & Thiemann, T. (1999). SL(2,R) model with two Hamiltonian constraints. *Physical Review D*, *60*(4).

**MLA:**

Montesinos, Merced, Carlo Rovelli, and Thomas Thiemann. "SL(2,R) model with two Hamiltonian constraints." *Physical Review D* 60.4 (1999).

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