A non-associative quaternion scalar field theory
arXiv:1211.5049 · doi:10.1142/S0217732313501630
Abstract
A non-associative Groenewold-Moyal plane is constructed using quaternion-valued function algebras. The symmetrized multi-particle states, the scalar product, the annihilation/creation algebra and d the formulation in terms of a Hopf algebra are also developed. Non-associative quantum algebras in terms of position and momentum operators are given as the simplest examples of a framework whose applications may involve string theory and non-linear quantum field theory
References in corpus (9)
- Gauge Symmetry and Supersymmetry of Multiple M2-Branes
- Algebraic structures on parallel M2-branes
- Modeling Multiple M2's
- Nonassociative Gravity in String Theory?
- Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
- Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry
- Twisted Poincaré Invariant Quantum Field Theories
- Octonions, G_2 and generalized Lie 3-algebras
- Non-associativity, supersymmetry and hidden variables
Cited by in corpus (6)
- Non-anti-hermitian quaternionic quantum mechanics
- Quaternionic scalar field in the real Hilbert space
- Quaternionic fermionic field
- Four-dimensional conformal field theory using quaternions
- Möbius transformation for left-derivative quaternion holomorphic functions
- Deformed angular momentum algebra within the real Hilbert space