Lowering and Raising Operators for the Orthogonal Group in the Chain O(n) ⊃ O(n − 1) ⊃ … , and their Graphs
dc.contributor.author | Pang, Sing-Chin | en_US |
dc.contributor.author | Hecht, Karl T. | en_US |
dc.date.accessioned | 2010-05-06T22:20:33Z | |
dc.date.available | 2010-05-06T22:20:33Z | |
dc.date.issued | 1967-06 | en_US |
dc.identifier.citation | Pang, Sing Chin; Hecht, K. T. (1967). "Lowering and Raising Operators for the Orthogonal Group in the Chain O(n) ⊃ O(n − 1) ⊃ … , and their Graphs." Journal of Mathematical Physics 8(6): 1233-1251. <http://hdl.handle.net/2027.42/70553> | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/70553 | |
dc.description.abstract | Normalized lowering and raising operators are constructed for the orthogonal group in the canonical group chain O(n) ⊃ O(n − 1) ⊃ … ⊃ O(2) with the aid of graphs which simplify their construction. By successive application of such lowering operators for O(n), O(n − 1), … on the highest weight states for each step of the chain, an explicit construction is given for the normalized basis vectors. To illustrate the usefulness of the construction, a derivation is given of the Gel'fand‐Zetlin matrix elements of the infinitesimal generators of O(n). | en_US |
dc.format.extent | 3102 bytes | |
dc.format.extent | 1071974 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | Lowering and Raising Operators for the Orthogonal Group in the Chain O(n) ⊃ O(n − 1) ⊃ … , and their Graphs | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Physics Department, University of Michigan, Ann Arbor, Michigan | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/70553/2/JMAPAQ-8-6-1233-1.pdf | |
dc.identifier.doi | 10.1063/1.1705340 | en_US |
dc.identifier.source | Journal of Mathematical Physics | en_US |
dc.identifier.citedreference | J. G. Nagel and M. Moshinsky, J. Math. Phys. 6, 682 (1965). | en_US |
dc.identifier.citedreference | M. Moshinsky, J. Math. Phys. 4, 1128 (1963); G. E. Baird and L. C. Biedenharn, 4, 1449 (1963). For earlier references consult these references. | en_US |
dc.identifier.citedreference | B. H. Flowers and S. Szpikowski, Proc. Phys. Soc. (London) 84, 193 (1964); J. C. Parikh, Nucl. Phys. 63, 214 (1965). J. N. Ginocchio, 74, 321 (1965); M. Ichimura, Progr. Theoret. Phys. (Kyoto) 32, 757 (1964); 33, 215 (1965). K. T. Hecht, Phys. Rev. 139, B794 (1965). | en_US |
dc.identifier.citedreference | B. H. Flowers and S. Szpikowski, Proc. Phys. Soc. (London) 84, 673 (1964). | en_US |
dc.identifier.citedreference | P. Kramer and M. Moshinsky, Nucl. Phys. 82, 241 (1966). | en_US |
dc.identifier.citedreference | I. M. Gel’fand and M. L. Zetlin, Dokl. Akad. Nauk. USSR 71, 1017 (1950). I. M. Gel’fand, R. A. Minlos, and Z. Ya. Shapiro Representations of the Rotation and Lorentz Groups and Their Application (The Macmillan Company, New York, 1963), p. 353. | en_US |
dc.identifier.citedreference | The Gel’fand‐Zetlin result has also been derived by algebraic techniques by J. D. Louck, Los Alamos Scientific Laboratory Reports LA 2451 (1960). | en_US |
dc.identifier.citedreference | G. Racah, CERN reprint 61‐8 (1961). | en_US |
dc.identifier.citedreference | The raising and lowering generators are not to be confused with the raising and lowering operators which are the subject of this paper. Except for O(3) the lowering and raising operators are complicated polynomial functions of the lowering and raising generators. | en_US |
dc.identifier.citedreference | A slight change has been made in the Gel’fand‐Zetlin notation. The first index has been shifted up by one unit so that mν1,mν1, mν2,mν2, … characterize the irreducible representation of O(v). The chain of numbers thus ends with m21m21 [irreducible representation of O(2)], rather than with m11m11. | en_US |
dc.identifier.citedreference | For the specific cases n = 5n=5 and 6 explicit expressions for raising and lowering operators have been given previously. J. Flores, E. Chacon, P. A. Mello, and M. de Llano, Nucl. Phys. 72, 352 (1965), and (n = 5)(n=5)K. T. Hecht, 63, 177 (1965). | en_US |
dc.identifier.citedreference | S. C. Pang, University of Michigan dissertation (to be published). | en_US |
dc.identifier.citedreference | † Note that O63O63 is an example of a neutral or zero‐step operator of type O2k,k.O2k,k. | en_US |
dc.identifier.citedreference | The superscript (2k+1)(2k+1) will be omitted whenever it is obvious. | en_US |
dc.owningcollname | Physics, Department of |
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