Testing non-associative quantum mechanics

Abstract

The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.

5 pages; v2: new references, extended discussion; v3: erratum included

References in corpus (6)

• Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7
• T-duality and closed string non-commutative (doubled) geometry
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Non-associative Deformations of Geometry in Double Field Theory
• Observing Monopoles in a Magnetic Analog of Ice
• States in non-associative quantum mechanics: Uncertainty relations and semiclassical evolution

Cited by in corpus (12)

• Non-geometric backgrounds in string theory
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Symplectic realisation of electric charge in fields of monopole distributions
• Magnetic monopoles and nonassociative deformations of quantum theory
• Weak associativity and deformation quantization
• Small magnetic charges and monopoles in non-associative quantum mechanics
• Monopole star products are non-alternative
• The ground state of non-associative hydrogen and upper bounds on the magnetic charge of elementary particles
• Moments and saturation properties of eigenstates
• Lagrangian formulation for electric charge in a magnetic monopole distribution
• Alternative multiplications and non-associativity in physics