1 research outputs found
The Frobenius formalism in Galois quantum systems
Quantum systems in which the position and momentum take values in the ring
and which are described with -dimensional Hilbert space, are
considered. When is the power of a prime, the position and momentum take
values in the Galois field , the position-momentum phase space is
a finite geometry and the corresponding `Galois quantum systems' have stronger
properties. The study of these systems uses ideas from the subject of field
extension in the context of quantum mechanics. The Frobenius automorphism in
Galois fields leads to Frobenius subspaces and Frobenius transformations in
Galois quantum systems. Links between the Frobenius formalism and Riemann
surfaces, are discussed