Odd Dimensional Translation between Complex and Quaternionic Quantum Mechanics | Zendy

Stefano De Leo | Zendy; P. Rotelli | Zendy

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Odd Dimensional Translation between Complex and Quaternionic Quantum Mechanics

Author(s) -

Stefano De Leo,

P. Rotelli

Publication year - 1996

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.96.247

Subject(s) - physics , translation (biology) , eigenvalues and eigenvectors , quaternionic representation , matrix (chemical analysis) , reduction (mathematics) , supersymmetric quantum mechanics , quantum mechanics , quantum , classical mechanics , complex matrix , quaternion , theoretical physics , pure mathematics , quantum statistical mechanics , geometry , mathematics , biochemistry , chemistry , chromatography , messenger rna , gene , materials science , composite material , irreducible representation , real representation

We complete the rules of translation between standard complex quantummechanics (CQM) and quaternionic quantum mechanics (QQM) with a complexgeometry. In particular we describe how to reduce ($2n$+$1$)-dimensionalcomplex matrices to {\em overlapping\/} ($n$+$1$)-dimensional quaternionicmatrices with generalized quaternionic elements. This step resolves anoutstanding difficulty with reduction of purely complex matrix groups withinquaternionic QM and avoids {\em anomalous} eigenstates. As a result we presenta more complete translation from CQM to QQM and viceversa.Comment: 7 pages, Revte

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