View Item 

Show simple item record

Structure of the Combinatorial Generalization of Hypergeometric Functions for SU(n) States
dc.contributor.authorWu, Alfred C. T.en_US
dc.date.accessioned2010-05-06T21:43:07Z
dc.date.available2010-05-06T21:43:07Z
dc.date.issued1971-03en_US
dc.identifier.citationWu, Alfred C. T. (1971). "Structure of the Combinatorial Generalization of Hypergeometric Functions for SU(n) States." Journal of Mathematical Physics 12(3): 437-440. <http://hdl.handle.net/2027.42/70155>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70155
dc.description.abstractThe combinatorics of the boson operator formalism in the construction of the SU(n) states provides a natural scheme for the appearance of certain generalized hypergeometric functions. It is shown that, while special cases exist where the functions thus generated belong to the class of generalized hypergeometric functions defined by Gel'fand et al. as being the Radon transforms of products of linear forms, the general cases apparently do not. This is already so at the SU(4) level.en_US
dc.format.extent3102 bytes
dc.format.extent257112 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleStructure of the Combinatorial Generalization of Hypergeometric Functions for SU(n) Statesen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Physics, University of Michigan, Ann Arbor, Michigan 48104en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70155/2/JMAPAQ-12-3-437-1.pdf
dc.identifier.doi10.1063/1.1665605en_US
dc.identifier.sourceJournal of Mathematical Physicsen_US
dc.identifier.citedreferenceAmong earlier references on the boson operator formalism, we mention the following: J. Schwinger, “On Angular Momentum,” U.S. Atomic Energy Commission Report NYO‐3071, 1952, reprinted in Quantum Theory of Angular Momentum, edited by L. C. Biedenharn and H. Van Dam (Academic, New York, 1965), p. 229; V. Bargmann and M. Moshinsky, Nucl. Phys. 18, 697 (1960); 23, 177 (1961); M. Moshinsky, 31, 384 (1962); Rev. Mod. Phys. 34, 813 (1962); J. Math. Phys. 4, 1128 (1963); also Refs. 2–4 below.en_US
dc.identifier.citedreferenceG. E. Baird and L. C. Biedenharn, J. Math. Phys. 4, 1449 (1963).en_US
dc.identifier.citedreferenceJ. G. Nagel and M. Moshinsky, J. Math. Phys. 6, 682 (1965).en_US
dc.identifier.citedreferenceM. Ciftan and L. C. Biedenharn, J. Math. Phys. 10, 221 (1969).en_US
dc.identifier.citedreferenceM. Ciftan, J. Math. Phys. 10, 1635 (1969).en_US
dc.identifier.citedreferenceI.e., a U(n)U(n) state such that it is a maximal state on the U(n−1)U(n−1) level; a maximal state is one where the entries in the Gel’fand pattern take on maximal values mij−1  =  mijmij−1=mij for j  =  2,⋯,nj=2,⋯,n and i  =  1,⋯,n−1.i=1,⋯,n−1.en_US
dc.identifier.citedreferenceI. M. Gel’fand and M. L. Zeltin, Doklady Akad. Nauk SSSR 71, 825 (1950).en_US
dc.identifier.citedreferenceFor similar considerations in the extension to the groups Sp(4)Sp(4) and O(5),O(5), see, e.g., W. J. Holman III, J. Math. Phys. 10, 1710 (1969).en_US
dc.identifier.citedreferenceE. P. Wigner, “Applications of Group Theory to the Special Functions of Mathematical Physics,” unpublished lecture notes, Princeton University, 1955.en_US
dc.identifier.citedreferenceN. J. Vilenkin, Special Functions and the Theory of Group Representations (Transl. Math. Mono. Vol. 22) (American Mathematical Society, Providence, R.I., 1968).en_US
dc.identifier.citedreferenceW. Miller, Jr., Lie Theory and Special Functions (Academic, New York, 1968).en_US
dc.identifier.citedreferenceJ. D. Talman, Special Functions—A Group Theoretic Approach (Benjamin, New York, 1968).en_US
dc.identifier.citedreferenceP. Appell and J. Kampé de Fériet, Fonctions hypergeometriques et hyperspheriques (Gauthier‐Villars, Paris, 1926), esp. Chap. 7; G. Lauricella, Rend. Circ. Mat. Palermo 7, 111 (1893).en_US
dc.identifier.citedreferenceL. J. Slater, Generalized Hypergeometric Functions (Cambridge U.P., Cambridge, 1966); esp. Chap. 8.en_US
dc.identifier.citedreferenceThe apparent twist in nomenclature may be unfortunate. The Lauricella function of the fourth kind, FD,FD, actually corresponds to the generalization of the Appell function of the first kind, F1,F1, to several variables.en_US
dc.identifier.citedreferenceI. M. Gel’fand, M. I. Graev, and N. Ya. Vilenkin, Generalized Functions (Academic, New York, 1966), Vol. V.en_US
dc.identifier.citedreferenceExcept, of course, the Appell function of the fourth kind, F4,F4, for which no analogous integral representation is known.en_US
dc.identifier.citedreferenceHere, the t1,t1, t2t2 integrals come from the F2F2 or the k1,k1, k2k2 sum; the t3t3 integral from the 2F12F1 or the k3k3 sum; finally the t4t4 integral from FD(3)FD(3) or the k4,k4, k5,k5, k6k6 sum.en_US
dc.owningcollnamePhysics, Department of


Files in this item

Name:
JMAPAQ-12-3-437-1.pdf
Size:
251.0KB
Format:
PDF
View/Open

Show simple item record

Remediation of Harmful Language

The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.

Accessibility

If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.