Abstract
When solving numerous quantum-mechanics problems, it becomes necessary to expand the irreducible representations (IR) of groups into irreducible components. The most straightforward way of solving this problem is to use the projection operators (PO).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. McDonald, Adv. Phys., 19, 371 (1961).
J. Shapiro, J. Math. Phys., 6, 1680 (1965).
R. M. Asherova, Yu. F. Smirnov, Uspekhi Matematicheskih Nauk, 24, 227 (1969);
Yu. F. Smirnov, in “Clustering Phenomena in Nuclei”, IAE A, Vienna, 1969, p. 153;
R. M. Asherova, Yu. F. Smirnov, V. N. Tolstoy, Theoreticheskaya i Matematicheskaya Fisika, 8, 255 (1971).
Yu. F. Smirnov, Thesis for Doctorate Degree, Inst. Nucl. Phys., Moscow State Univ., 1971.
R. M. Asherova, Yu. F. Smirnov, V. N. Tolstoy, Preprint FEI-397, Obninsk, 1973.
A. N. Leznov, M. V. Saveliev, Functional Analysis, 8, 87 (1974); Preprint IFVE STF-74–46, Serpuhkhov, 1974.
A. N. Leznov, M. V. Saveliev, Elem. Part. Atom. Nuclei, 7, 55 (1976); Theoreticheskaya i Matematicheskaya Fisika, 31, 273 (1977).
R. M. Asherova, Yu. F. Smirnov. V. N. Tolstoy, Theoreticheskaya i Matematicheskaya Fisika, 15, 107 (1973).
V. N. Tolstoy, Thesis for Candidate Degree, Inst. Nucl. Phys., Moscow State University, 1972;
Yu. F. Smirnov, Preprint ITF-75–45, Kiev, 1975.
V. A. Mishukov, Graduation Thesis, Dept. Phys., Moscow State Univ., 1973.
Yu. F. Smirnov, V. N. Tolstoy, Rept. Math. Phys., 4, 105 (1973).
Yu. F. Smirnov, V. N. Tolstoy, Preprint ITF-75–90R, Kiev, 1975.
R. M. Asherova, Yu. F. Smirnov. V. N. Tolstoy, Preprint FEI-424, Obninsk, 1973; J. Phys. (G), 4, 205 (1978).
R. M. Asherova, Yu. F. Smirnov, Nucl. Phys. A144, 116 (1970); Rept. Math. Phys., 4, 83 (1973).
D. T. Sviridov, Yu. F. Smirnov, V. N. Tolstoy, Dokl. Akad. Nauk SSSR, 206, 53 (1972); Rept. Math. Phys., 7, 349 (1975);
D. T. Sviridov, Yu. F. Smirnov, Theory of Optical Spectra of Transition Metals, Nauka, Moscow, 1977 (in Russian).
R. M. Asherova, Yu. F. Smirnov, Nucl. Phys. B4, 399 (1968).
V. A. Knyr, Yu. F. Smirnov, V. N. Tolstoy, Rept. Math. Phys., 8, 343 (1975).
J. P. Draayer, J. Math. Phys., 11, 3225 (1970).
E. Norvaisas, S. Alisauskas, Liet. fiz. Rink, 17, 457 (1977).
I. M. Gelfand, M. L. Tsetlin, Dokl, Akad. Nauk SSSR, 71, 825 (1970); 71, 1017 (1950).
V. A. Knyr, P. P. Pipiraite, Yu. F. Smirnov, Sov. Nucl. Phys. 22, 1063 (1975).
Yu. F. Smirnov, K. V. Shitikova, Elem. Part. Atomic Nuclei, 8, 847 (1977).
N. Ya. Vilenkin, Special Functions and the Theory of Group Representation, Fizmatgiz, Moscow, 1965.
J. Patera, F. Stenger, Preprint CRM-199, Univ. Montreal, 1972.
N. Mukunda, B. Radhakrishnan, J. Math. Phys., 15, 1332, 1643, 1656 (1974).
Yu. A. Smorodinsky, I. A. Verdiev, G. A. Kerimov, Sov. Nuc1. Phys., 20, 827 (1974).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Plenum Press, New York
About this chapter
Cite this chapter
Smirnov, Y.F. (1980). Projections Operators for Semisimple Compact Lie Groups and their Applications. In: Gruber, B., Millman, R.S. (eds) Symmetries in Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3833-8_26
Download citation
DOI: https://doi.org/10.1007/978-1-4684-3833-8_26
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-3835-2
Online ISBN: 978-1-4684-3833-8
eBook Packages: Springer Book Archive