Path integral for the quantum baker's map

Abstract

We derive a formally exact sum of path integrals for the quantum propagator of the baker's transformation. The phases depend only on the classical actions as in usual phase space path integrals and the sums are over all the symbolic orbits. The deduction depends on multiple Poisson transformations, which lead to a further infinite sum of integrals, but our computations for the propagator and its trace for two iterations show that this is rapidly convergent. Explicit formulae for the quantum corrections to the semiclassical propagator are presented for this case.