Coherent states on quaternion slices and a measurable field of Hilbert spaces

JOURNAL OF GEOMETRY AND PHYSICS

卷:110

Article

Muraleetharan, B.¹  Thirulogasanthar, K.² 

[1] Univ Jaffna, Dept Math & Stat, Thirunelveli, Jaffna, Sri Lanka

[2] Concordia Univ, Dept Comp Sci & Software Engn, 1455 de Maisonneuve Blvd West, Montreal, PQ H3G 1M8, Canada

关键词: Quaternion;    Coherent state;    Reproducing kernel;    Group representation;    Direct integral;   

DOI  :  10.1016/j.geomphys.2016.08.006

来源: Elsevier

【 摘 要 】

A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral appears again as a reproducing kernel Hilbert space for a bigger Hilbert space over the whole quaternions. Hilbert spaces over quaternion slices are identified as representation spaces for a set of irreducible unitary group representations and their direct integral is shown to be a reducible representation for the Hilbert space over the whole quaternion field. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free