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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 1 — Jan. 1, 2007
  • pp: 204–210

Pauli algebraic forms of normal and nonnormal operators

Tiberiu Tudor and Aurelian Gheondea  »View Author Affiliations


JOSA A, Vol. 24, Issue 1, pp. 204-210 (2007)
http://dx.doi.org/10.1364/JOSAA.24.000204


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Abstract

A unified treatment of the Pauli algebraic forms of the linear operators defined on a unitary linear space of two dimensions over the field of complex numbers C 1 is given. The Pauli expansions of the normal and nonnormal operators, unitary and Hermitian operators, orthogonal projectors, and symmetries are deduced in this frame. A geometrical interpretation of these Pauli algebraical results is given. With each operator, one can associate a generally complex vector, its Pauli axis. This is a natural generalization of the well-known Poincaré axis of some normal operators. A geometric criterion of distinction between the normal and nonnormal operators by means of this vector is established. The results are exemplified by the Pauli representations of the normal and nonnormal operators corresponding to some widespread composite polarization devices.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(260.5430) Physical optics : Polarization

ToC Category:
Physical Optics

History
Original Manuscript: March 17, 2006
Revised Manuscript: June 18, 2006
Manuscript Accepted: July 3, 2006

Citation
Tiberiu Tudor and Aurelian Gheondea, "Pauli algebraic forms of normal and nonnormal operators," J. Opt. Soc. Am. A 24, 204-210 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-1-204


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