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  • 1
    Electronic Resource
    Electronic Resource
    Clebsch–Gordan coefficients and related identities obtained by an integration over the group space of SUq(2) (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 1912-1933 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Clebsch–Gordan coefficients of SUq(2) are here calculated by an integration over the group manifold following the Woronowicz prescription. A representation is obtained that is different from the one derived from the q-group algebra. The equivalency of the two results implies a q-identity and establishes a relation between q-hypergeometric functions. In the limit q=1, our result gives a different expression for the Clebsch–Gordan coefficients of SU(2), and the q-identity relation reduces to an identity between binomial coefficients. The Woronowicz technique is extended to calculate the integral of the product of many irreducible representations. A summary of the main results has already been presented elsewhere. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531094
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  • 2
    Electronic Resource
    Electronic Resource
    Dyons in affine field theories (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2674-2682 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: By postulating that the gauge vector field and the Higgs field both lie in an affine algebra rather than a Lie algebra, an affine field theory with an expanded soliton sector is obtained. An infinite family of exact, special solutions of the new equations corresponding to the original 't Hooft–Polyakov solitonic solutions, is now found. A perturbation method for an arbitrary solution of the new equation is also proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528499
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  • 3
    Electronic Resource
    Electronic Resource
    q deformations of the oscillator (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 4259-4266 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Generating functions that interpolate between the generating functions for Hermitian multilinears and the corresponding Grassmann multilinears are considered. The new functions that arise in this way may be related to state functions of q-deformed harmonic oscillators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529827
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  • 4
    Electronic Resource
    Electronic Resource
    The q-Coulomb problem in configuration space (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 3675-3683 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We formulate the q-Coulomb problem in configuration space with the aid of ladder operators for the radial wave function. The highest angular momentum state corresponding to the principal quantum number n is found to be the monomial rn−1 multiplied by a q-exponential. The states of lower angular momentum are q-associated Laguerre polynomials multiplied by the same q-exponential. The state functions all lie in the complex plane and may be interpreted in the standard way. The energy levels are again given by a Balmer formula with n replaced by the basic n. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531594
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  • 5
    Electronic Resource
    Electronic Resource
    q-Deformation of the Coulomb problem (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3273-3284 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The hydrogenic Schrödinger equation may be transformed into an integral equation on the group space of SO(3). The solutions of this integral equation are the Wigner functions Djmn, the matrix elements of the irreducible representations of SO(3). In this article we examine a q-deformation of the Coulomb problem for which the new wave functions are the matrix elements of the irreducible representations of the quantum group SUq(2). The new integral equation is formulated in terms of the Woronowicz integral. The eigenvalues are given by a modified Balmer formula which lifts the Coulomb degeneracy and replaces n by [n].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530466
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  • 6
    Electronic Resource
    Electronic Resource
    The GL q (2) gauge theory (1993)
    Springer
    Letters in mathematical physics 29 (1993), S. 75-82 
    Details
    ISSN: 1573-0530
    Keywords: 81T13 ; 83E99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We present some partial results on theq-deformation of the GL(2) Yang-Mills theory. In particular, the irreducible representations needed to describe the complete set of physical states are obtained by a simple procedure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00760861
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  • 7
    Electronic Resource
    Electronic Resource
    q-transformation theory (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 221-227 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 81S05 ; 81P99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU q (2) algebra. To obtain transition probabilities, one must take the ‘Woronowicz square.’
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00761294
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  • 8
    Electronic Resource
    Electronic Resource
    Spontaneous symmetry breaking of affine field theory (1989)
    Springer
    Letters in mathematical physics 17 (1989), S. 157-164 
    Details
    ISSN: 1573-0530
    Keywords: 17B67 ; 81G20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is possible to construct non-Abelian field theories by gauging Kac-Moody algebras. Here we discuss the spontaneous symmetry breaking of such theories via the Higgs mechanism. If the Higgs particle lies in the Cartan subalgebra of the Kac-Moody algebra, the previously massless vectors acquire a mass spectrum that is linear in the Kac-Moody index and has additional fine structure depending on the associated Lie algebra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402330
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  • 9
    Electronic Resource
    Electronic Resource
    Integration over the group space of SUq(2), Clebsch-Gordan coefficients, and related identities (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 221-229 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We calculate the Clebsch-Gordan coefficients of SUq(2) by a Woronowicz integration over the group manifold and obtain a representation differing from that reached by working with theq-group algebra. These apparently different results must agree, however, and their equivalence implies aq-identity. On lettingq = 1, we shall obtain two results of different structures for the Clebsch-Gordan coefficients of SU(2) and their equivalence similarly implies an identity among the usual binomial coefficients. With the same approach, one may extend the Woronowicz integral of the product of two irreducible representations to products of many irreducible representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749623
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  • 10
    Electronic Resource
    Electronic Resource
    Gauged Kac-Moody algebras (1988)
    Springer
    Letters in mathematical physics 16 (1988), S. 279-285 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct a non-Abelian field theory by gauging a Kac-Moody algebra. One obtains an infinite tower of interacting vector fields and associated ghosts obeying slightly modified Feynman rules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398966
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