Spherical Harmonics Y l m ( θ , ϕ ) : Positive and Negative Integer Representations of su ( 1,1 ) for l - m and l + m
Author
Source
Advances in High Energy Physics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-03-10
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
The azimuthal and magnetic quantum numbers of spherical harmonics Y l m ( θ , ϕ ) describe quantization corresponding to the magnitude and z -component of angular momentum operator in the framework of realization of s u ( 2 ) Lie algebra symmetry.
The azimuthal quantum number l allocates to itself an additional ladder symmetry by the operators which are written in terms of l .
Here, it is shown that simultaneous realization of both symmetries inherits the positive and negative ( l - m ) - and ( l + m ) -integer discrete irreducible representations for s u ( 1,1 ) Lie algebra via the spherical harmonics on the sphere as a compact manifold.
So, in addition to realizing the unitary irreducible representation of s u ( 2 ) compact Lie algebra via the Y l m ( θ , ϕ ) ’s for a given l , we can also represent s u ( 1,1 ) noncompact Lie algebra by spherical harmonics for given values of l - m and l + m .
American Psychological Association (APA)
Fakhri, H.. 2016. Spherical Harmonics Y l m ( θ , ϕ ) : Positive and Negative Integer Representations of su ( 1,1 ) for l - m and l + m. Advances in High Energy Physics،Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1095182
Modern Language Association (MLA)
Fakhri, H.. Spherical Harmonics Y l m ( θ , ϕ ) : Positive and Negative Integer Representations of su ( 1,1 ) for l - m and l + m. Advances in High Energy Physics No. 2016 (2016), pp.1-7.
https://search.emarefa.net/detail/BIM-1095182
American Medical Association (AMA)
Fakhri, H.. Spherical Harmonics Y l m ( θ , ϕ ) : Positive and Negative Integer Representations of su ( 1,1 ) for l - m and l + m. Advances in High Energy Physics. 2016. Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1095182
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095182