A non-associative quaternion scalar field theory
Sergio Giardino, Paulo Teot\^onio-Sobrinho
TL;DR
This paper develops a non-associative quaternion scalar field theory using quaternion-valued functions, exploring algebraic structures and potential applications in string theory and non-linear quantum fields.
Contribution
It introduces a non-associative Groenewold-Moyal plane and constructs related algebraic frameworks and examples, expanding the mathematical foundation of quantum field theories.
Findings
Constructed a non-associative Groenewold-Moyal plane
Developed symmetrized multi-particle states and scalar products
Presented non-associative quantum algebras with potential physical applications
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
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