A Parity-Conserving Canonical Quantization for the Baker’s Map

We present here a complete description of the quantization of the baker’s map. The method we use is quite different from that used in Balazs and Voros [BV] and Saraceno [S]. We use as the quantum algebra of observables the operators generated by {exp (2πix̂) , exp (2πip̂)} and construct a unitary propagator such that as ~ → 0, the classical dynamics is returned. For Planck’s constant h = 1/N , we show that the dynamics can be reduced to the dynamics on an N -dimensional Hilbert space, and the unitary N × N matrix propagator is the same as given in [BV] except for a small correction of order h. This correction is is shown to preserve the symmetry x → 1− x and p → 1− p of the classical map for periodic boundary conditions.