Spin and rotations in Galois field quantum mechanics. (English) Zbl 1263.81021
Summary: We discuss the properties of Galois field quantum mechanics constructed on a vector space over the finite Galois field \(GF(q)\). In particular, we look at two-level systems analogous to spin, and discuss how \(SO(3)\) rotations could be embodied in such a system. We also consider two-particle ‘spin’ correlations and show that the Clauser-Horne-Shimony-Holt inequality is nonetheless not violated in this model.
MSC:
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 81P15 | Quantum measurement theory, state operations, state preparations |
| 46S10 | Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis |
| 11S20 | Galois theory |
