Non-commutative solitons in finite quantum mechanics

Non-commutative Solitons in Finite Quantum Mechanics

The continuous Lorentz symmetry is broken to a discrete subgroup–but the internal (gauge) symmetry is preserved. Note that it is this feature that renders the study of lattice supersymmetry so non-trivial, since supersymmetry mixes Lorentz symmetry and internal symmetry in a non-trivial way. In quantum mechanics we consider functions that take values in phase space. These functions are valued i...

Non-commutative Spheres and Numerical Quantum Mechanics

We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations. The C∗algebras associated with the discretized CCRs are the non-commutative spheres of Bratteli, Elliott, Evans and Kishimoto. 1991 Mathematics Subject Classification. Primary 46L40;...

Quantum-like Classical Mechanics in Non-commutative Phase Space

Quantum-like evolution laws for observables can be derived from classical Hamiltonian equations with the only additional assumption that the phase space is non-commutative. The derivation is possible for Hamiltonians that are polynomial functions in position and momentum variables, and supports the use of phase space distributions functions in both quantum and classical theories that rely on ex...

Quantum Mechanics: Harbinger of a Non-commutative Probability Theory?

In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to see the structure of quantum processes in terms of non-commutative probability theory, a non-Boolean structure of the implicate order which contains Boolean...

‘non – Hilbertian’ Quantum Mechanics on the Finite