Quantum Mechanics With Noncommutative Amplitudes

Abstract

We formulate a Born rule for families of quantum systems parametrized by a noncommutative space of control parameters. The resulting formalism may be viewed as a generalization of quantum mechanics where overlaps take values in a noncommutative algebra, rather than in the complex numbers.

50 pages, 2 figures

References in corpus (6)

• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• The Uncertainty of Fluxes
• Quantum Mechanics Without State Vectors
• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• Computing the distance between quantum channels: Usefulness of the Fano representation
• The Jordan formulation of Quantum Mechanics: a review

Cited by in corpus (2)

• A Comment On Berry Connections
• Homological Tools for the Quantum Mechanic