The quaternionic scalar field

This paper presents a novel and comprehensive canonical quantization of the quaternionic scalar field within Minkowski spacetime, addressing challenges and inconsistencies observed in the quaternionic scalar field quantization, particularly regarding micro-causality. Using basic mathematical concepts, we develop a rigorous framework for a scalar field that preserves its quaternionic nature throughout the quantization process. This paper derives the full Lagrangian density, field equations and, crucially, obtains the explicit expressions for the Hamiltonian and momentum operators for the quaternionic scalar field. While quaternionic formalisms can offer alternative perspectives on known physical models, this study focuses on establishing a consistent quantization procedure for a quaternionic field as an entity, thereby rectifying the theoretical discrepancies and laying groundwork for further exploration into models where the noncommutative structure of quaternions may lead to novel physical insights or more compact descriptions of fundamental quaternionic fields.