Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Group theoretical basis of some identities for the generalized hypergeometric series (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 497-508 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that Thomae's identity between two 3F2 hypergeometric series of unit argument together with the trivial invariance under separate permutations of numerator and denominator parameters implies that the symmetric group S5 is an invariance group of this series. A similar result is proved for the terminating Saalschützian 4F3 series, where S6 is shown to be the invariance group of this series (or S5 if one parameter is eliminated by using the Saalschütz condition). Here Bailey's identity is realized as a permutation of appropriately defined parameters. Finally, the set of three-term relations between 3F2 series of unit argument discovered by Thomae [J. Thomae, J. Reine Angew. Math. 87, 26 (1879)] and systematized by Whipple [F. J. Whipple, Proc. London Math. Soc. 23, 104 (1925)] is shown to be transformed into itself under the action of the group S6×Λ, where Λ is a two-element group. The 12 left cosets of S6×Λ with respect to the invariance group S5 are the structural elements underlying the three-term relations. The symbol manipulator macsyma was used to obtain preliminary results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527634
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Weight-2 zeros of 3j coefficients and the Pell equation (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2812-2823 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: All weight-2 zeros of the Wigner 3j coefficients may be obtained from the quadratic Diophantine equation known as Pell's equation. These zeros may then be classified by the orbits of a discrete, infinite-order subgroup of the Lorentz group SO(1,1). This is carried out by transforming the "polynomial part'' of a weight-2 3j coefficient to Pellian form and obtaining the fundamental zeros numerically. The relation of this polynomial to a family of binary quadratic forms is also given, together with a discussion of the invariance group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527731
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On the denominator function for canonical SU(3) tensor operators. II. Explicit polynomial form (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1106-1117 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The canonical resolution of the multiplicity problem for tensor operators in SU(3) is equivalent to the map (the denominator mapping) from the set of all SU(3) unit tensor operators to SU(3) invariant functions (the denominator functions). The denominator function vanishes precisely on that characteristic null space that specifies each operator uniquely since [for SU(3)] the characteristic null spaces are known to be simply ordered. Each denominator function can be expressed, up to explicitly known multiplicative factors, as a ratio of two successive polynomials in the set {Gtq}, t=0,1,..., q+1, q=0,1,... . By obtaining explicitly the set of all polynomials {Gtq}, this paper completes the construction of all SU(3) denominator functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527949
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Zeros of Racah coefficients and the pell equation (1986)
    Springer
    Acta applicandae mathematicae 7 (1986), S. 257-311 
    Details
    ISSN: 1572-9036
    Keywords: 10 B05 ; 20C35 ; 33A30 ; 81-47 ; 81G30 ; Racah coefficients ; Clebsch-Gordan coefficients ; weight 2 zeros ; Pell equations ; Diophantine equations ; orbit classification of zeros ; symbolic formula manipulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The interface between Racah coefficients and mathematics is reviewed and several unsolved problems pointed out. The specific goal of this investigation is to determine zeros of these coefficients. The general polynomial is given whose set of zeros contains all nontrivial zeros of Racah (6j) coefficients [this polynomial is also given for the Wigner-Clebsch-Gordan (3j) coefficients]. Zeros of weight 1 3j- and 6j-coefficients are known to be related to the solutions of classic Diophantine equations. Here it is shown how solutions of the quadratic Diophantine equation known as Pell's equation are related to weight 2 zeros of 3j- and 6j-coefficients. This relation involves transformations of quadratic forms over the integers, the orbit classification of zeros of Pell's equation, and an algorithm for determining numerically the fundamental solutions of Pell's equation. The symbol manipulation program MACSYMA was used extensively to effect various factorings and transformations and to give a proof.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047095
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    The symplecton: A prototype for semi-simple graded Lie algebras (1976)
    Springer
    Letters in mathematical physics 1 (1976), S. 233-235 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An elementary, physically motivated, example of a semi-simple graded Lie algebra (SSGLA) is shown to be given by the ‘symplecton realization’ of angular momentum [an associative, involutive, inner-product algebra whose characteristic polynomials realize the symplectic group Sp(2)]. The Pais-Rittenberg result shows that the n-component symplecton realizes the most general, SSGLA, Sp(2n).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00417609
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    A pattern calculus for tensor operators in the unitary groups (1968)
    Springer
    Communications in mathematical physics 8 (1968), S. 89-131 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract For a large class of tensor operators inU(n), a surprisingly simple diagrammatic calculus of patterns is shown to exist; to each operator of this class a pattern may be assigned in terms of which thecomplete algebraic formula for all matrix elements may be read off directly. The class of operators includes all fundamental, elementary and extremal Wigner operators in allU(n). Application of the pattern calculus toward the explicit determination of all tensor operators is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01645800
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    A kinematical model for quarks and hadrons (1972)
    Springer
    Foundations of physics 2 (1972), S. 149-159 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Starting from simple topological arguments due to Dirac on the classical rotational properties of extended rigid bodies, we abstract the concept of a finite-size spinor (FSS). The FSS is a concept distinct from both point spinors (e.g., electrons) and composite spinors (e.g., nuclei), and suggests a new model for baryons. The FSS offers a natural explanation of “threeness” for the quarks, excludes the existence of free quarks, denies the operational definition of quark spin statistics, and, moreover, leads to the dual model of hadronic interactions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00708498
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...