G. G. Emch, H. Narnhofer, W. Thirring, G. L. Sewell
Anosov Actions on Non--commutative Algebras
The paper is published: J. Math. Phys. 35, 11 (1994) 5582-5599

MSC:

58F15 Hyperbolic structures (expanding maps, Anosov systems, etc.)

81S10 Geometric quantization, symplectic methods, See Also {

58F06 Geometric quantization (applications of representation theory), See also {22E45, 81S10}

83C47 Quantum field theory aspects, See also {81T20}

Abstract: We construct an axiomatic framework for a quantum mechanical
extension to the theory of Anosov systems, and show that this
retains some of the characteristic features of its classical
counterpart, e.g. positive Lyapunov exponents, a vectorial
K--property, and exponential clustering. We then investigate
the effects of quantisation
on two prototype examples of Anosov systems, namely the
iterations of an automorphism of the torus (the `Arnold Cat'
model) and the free dynamics of a particle on a surface of
negative curvature. It emerges that the
Anosov property survives quantisation in the case of the former
model, but not of the latter one. Finally, we show that the
modular dynamics of a relativistic quantum field on the Rindler
wedge of Minkowski space is that of an Anosov system.

Keywords: Anosov systems, quantization, modular dynamics, relativistic quantum field