Coherent state Quantization of quaternions
B. Muraleetharan, K. Thirulogasanthar
TL;DR
This paper develops a quaternionic quantum mechanics framework by extending coherent state quantization methods from complex to quaternionic fields, including the harmonic oscillator and Weyl-Heisenberg algebra.
Contribution
It introduces a quaternionic coherent state quantization approach, deriving quaternionic harmonic oscillator and Weyl-Heisenberg algebra, expanding the mathematical foundation of quaternionic quantum mechanics.
Findings
Quaternionic coherent states are constructed and analyzed.
Quaternionic harmonic oscillator and Weyl-Heisenberg algebra are formulated.
Quantization of quaternionic fields is achieved using upper and lower symbols.
Abstract
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and related quantities are analysed. Quaternionic version of the harmonic oscillator and Weyl-Heisenberg algebra are also obtained.
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