Monopole star products are non-alternative

Abstract

Non-associative algebras appear in some quantum-mechanical systems, for instance if a charged particle in a distribution of magnetic monopoles is considered. Using methods of deformation quantization it is shown here, that algebras for such systems cannot be alternative, i.e. their associator cannot be completely anti-symmetric.

14 pages

References in corpus (5)

• A field-theory motivated approach to symbolic computer algebra
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• Towards a Theory of Nonassociative Gravity
• States in non-associative quantum mechanics: Uncertainty relations and semiclassical evolution
• Weak associativity and deformation quantization

Cited by in corpus (6)

• Non-geometric backgrounds in string theory
• Nonassociative differential geometry and gravity with non-geometric fluxes
• Magnetic monopoles and nonassociative deformations of quantum theory
• Nearly associative deformation quantization
• Non-commutative gauge symmetry from strong homotopy algebras
• Lagrangian formulation for electric charge in a magnetic monopole distribution