Odd Dimensional Translation between Complex and Quaternionic Mechanics

Abstract

We complete the rules of translation between standard complex quantum mechanics (CQM) and quaternionic quantum mechanics (QQM) with a complex geometry. In particular we describe how to reduce ($2n$+$1$)-dimensional complex matrices to {\em overlapping\/} ($n$+$1$)-dimensional quaternionic matrices with generalized quaternionic elements. This step resolves an outstanding difficulty with reduction of purely complex matrix groups within quaternionic QM and avoids {\em anomalous} eigenstates. As a result we present a more complete translation from CQM to QQM and viceversa.

7 pages, Revtex

References in corpus (1)

• Duffin-Kemmer-Petiau equation on the quaternion field

Cited by in corpus (8)

• Right eigenvalue equation in quaternionic quantum mechanics
• Quaternionic differential operators
• Octonionic Quantum Mechanics and Complex Geometry
• Asymptotic Redundancies for Universal Quantum Coding
• Quaternions in mathematical physics (1): Alphabetical bibliography
• Quaternionic Electroweak Theory and CKM Matrix
• Half-whole Dimensions in Quaternionic Quantum Mechanics
• The quaternionic determinat