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

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Cited by in corpus (3)

• Energy Observable for a Quantum System with a Dynamical Hilbert Space and a Global Geometric Extension of Quantum Theory
• A Comment On Berry Connections
• Homological Tools for the Quantum Mechanic