Odd Dimensional Translation between Complex and Quaternionic Mechanics

Details Odd Dimensional Translation between Complex and Quaternionic Mechanics Odd Dimensional Translation between Complex and Quaternionic Mechanics

1996-05-03

arxiv.org/abs/hep-th/9605021v1

Prog.Theor.Phys. 96 (1996) 247-256

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, Revtex

Scientific paper

10.1143/PTP.96.247

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.

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