Half-whole Dimensions in Quaternionic Quantum Mechanics
Stefano De Leo (Dip. di Fisica, INFN, Lecce)
TL;DR
This paper introduces half-whole dimensions for quaternionic matrices and develops a quaternionic Frobenius-Schur theorem to determine the correct dimensionality of representations in quaternionic quantum mechanics.
Contribution
It proposes a novel quaternionic dimensionality concept and extends the Frobenius-Schur theorem to quaternionic matrices, aiding in representation theory.
Findings
Defined half-whole dimensions for quaternionic matrices
Extended Frobenius-Schur theorem to quaternionic context
Determined proper quaternionic dimensions for Dirac and DKP algebra representations
Abstract
We introduce {\em half-whole} dimensions for quaternionic matrices and propose a quaternionic version of the Frobenius-Schur theorem which allows us to obtain the proper quaternionic dimensionality for the representations of the Dirac and Duffin-Kemmer-Petiau (DKP) algebras.
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