Abstract
In his pioneering 1989 paper1 on the q-oscillator realization of quantum algebras,2 Larry Biedenharn also defined the q-analogue coherent states lz>q and pointed out the physically important property that the ΔQ ΔP uncertainty relation increases with n in the number basis ln>q for q ≠ 1. In this paper, we will review (i) the use of these q-analogue coherent states to investigate the properties of the q-analogue quantized field in the lz>q “classical limit” paralleling conventional quantum optics analyses, and review (ü) the fractional uncertainties and uncertainty relations of various physical quantities characterizing the q-analogue quantized field in this limit.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
L. Biedenharn, J. Phys. A22, L873 (1989).
A. Macfarlane, J. Phys. A22, 4581 (1989)
C.-P. Sun and H.-C. Fu, J. Phys. A22, L983(1989)
M. Chaichian and P. Kulish, Phys. Lett. B234, 72 (1990).
R.W. Gray and C.A. Nelson, J. Phys. A23, L945 (1990)
A.J. Bracken, D.S. McAnally, R.B. Zhang and M.D. Gould, J. Phys. A24, 1379 (1991)
B. Jurco, Lett. Math. Phys. 21, 51 (1991).
R.J. Glauber, Phys. Rev. 131, 2766 (1963)
E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).
S.-H. Chiu, R.W. Gray, C.A. Nelson, Phys. Lett. A164, 237 (1992); S.-H. Chiu, M. Fields, CA. Nelson, unpublished.
M. Fields and CA. Nelson, SUNY BING 7/27/92.
L. Susskind and J. Glogower, Physics 1, 49 (1964).
W.H. Louisell, Phys. Lett. 7, 60 (1963).
P.A. Dirac, Proc. Royal Soc. London A114, 243 (1927); W. Heitler, “Quantum Theory of Radiation”, p. 65 (Oxford U. Press, 1954).
P.W. Anderson, “Basic Notions of Condensed Matter Physics”, p. 229 (Addison-Wesley, 1984).
P. Carruthers and M.M. Nieto, Phys. Rev. Lett. 14, 387 (1965); Rev. Mod. Phys. 40, 411(1968)
R. Jackiw, J. Math. Phys. 9, 339(1968)
J.W. Noh, A. Fongeres, and L. Mandel, Phys. Rev. Lett. 67, 1426 (1991).
D.T. Pegg and S.M. Barnett, Europhys. Lett. 6, 483 (1988); J. Mod. Opt. 36, (1989)
R. Lynch, Phys. Rev. A41, 2841 (1990).
M. Chaichian and D. Ellinas, J. Phys. A23, L291 (1990).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Nelson, C.A. (1993). Novel Implications of the q-Analogue Coherent States. In: Gruber, B. (eds) Symmetries in Science VI. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1219-0_44
Download citation
DOI: https://doi.org/10.1007/978-1-4899-1219-0_44
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1221-3
Online ISBN: 978-1-4899-1219-0
eBook Packages: Springer Book Archive