On the multiplicativity of quantum cat maps

TL;DR

This paper investigates the quantum propagators of linear automorphisms of the two-torus, known as cat maps, establishing a proper representation of the theta group and providing explicit formulas for these propagators.

Contribution

It proves the existence of a phase choice that yields a true representation of the theta group and derives explicit formulas for the quantum propagators.

Findings

Existence of a phase choice for proper representation

Explicit formulas for quantum propagators

Connection to Weil's representation

Abstract

The quantum mechanical propagators of the linear automorphisms of the two-torus (cat maps) determine a projective unitary representation of the theta group, known as Weil's representation. We prove that there exists an appropriate choice of phases in the propagators that defines a proper representation of the theta group. We also give explicit formulae for the propagators in this representation.