Baker映射的宇称守恒正则量子化
A Parity-Conserving Canonical Quantization for the Baker's Map
摘要：
我们在这里提出了一个完整的描述量化的面包师的地图。我们使用的方法与Balazs和Voros [BV]和Saraceno [S]中使用的方法完全不同。我们使用{exp（2 Pi ix），exp（2 Pi ip）}生成的算子作为可观测量的量子代数，并构造一个酉传播子，使得当普朗克常数趋于零时，经典动力学返回。当Planck常数满足1/N且N为偶数的积分条件时，当环面上的波函数满足周期性边界条件时，我们证明了动力学可以归结为N维Hilbert空间上的动力学，并且除了对Planck常数阶数作了小的修正外，酉N × N矩阵传播子与文献[BV]中给出的相同.这种修正被证明是保持对称性x->1-x和p->1-p的经典映射的周期边界条件。
英文摘要：
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(2 Pi ix),exp (2 Pi ip)} and construct a unitary propagator such that as Planck's constant tends to zero,the classical dynamics is returned. For Planck's constant satisfying the integrality condition 1/N with N even, and for periodic boundary conditions for the wave functions on the torus, we show that the dynamics can be reduced to the dynamics on an N-dimensional Hilbert space, and the unitary N by N matrix propagator is the same as given in [BV] except for a small correction of order Planck's constant. This correction is is shown to preserve the symmetry x->1-x and p->1-p of the classical map for periodic boundary conditions.
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