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
    Multiplicity, invariants, and tensor product decompositions of compact groups (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 6468-6485 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Decomposing tensor products of irreducible representations of compact groups almost always involves multiplicity, wherein some irreducible representations occur more than once in the direct sum decomposition. We show that the multiplicity can always be specified by polynomial group invariants. The setting is a Bargmann–Segal–Fock space in n×N complex variables, where n is the number of labels needed to specify the tensor product and N is the dimension of the fundamental representation of the compact group. Both the tensor product and direct sum bases are realized as polynomials in this space, and it is shown how Clebsch–Gordan and Racah coefficients can be computed by suitably differentiating these polynomials. The example of SU(N) is discussed in detail, and it is shown that the multiplicity can be computed as the solution of certain diophantine equations arising from powers of group invariants, namely minors of determinants. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531787
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The quartic anharmonic oscillator and its associated nonconstant magnetic field (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4887-4899 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quantum mechanical anharmonic oscillators and Hamiltonians for particles in external magnetic fields are related to representations of nilpotent groups. Using this connection the eigenfunctions of the quartic anharmonic oscillator with potential Vα(x)=(α+(x2/2))2 can be used to determine the eigenfunctions of a charged particle in a nonconstant magnetic field, of the form Bz=β2+β3x. The quartic anharmonic oscillator eigenvalues for low-lying states are obtained numerically and a function which interpolates between α(very-much-less-than)0 (a double harmonic oscillator) and α(very-much-greater-than)0 (a harmonic oscillator) is shown to give a good fit to the numerical data. Approximate expressions for the quartic anharmonic oscillator eigenfunctions are then used to get the eigenfunctions for the magnetic field Hamiltonian. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531924
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Orthogonal polynomial bases of the orthogonal and symplectic groups (1982)
    Springer
    Czechoslovak journal of physics 32 (1982), S. 499-503 
    Details
    ISSN: 1572-9486
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The explicit construction of orthogonal polynomial bases of the orthogonal groups in a Gelfand-Cetlin basis is given. An indication how to compute orthogonal bases for the symplectic groups is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01596839
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Dual pairs and representations of scattering amplitudes (1987)
    Springer
    Czechoslovak journal of physics 37 (1987), S. 329-337 
    Details
    ISSN: 1572-9486
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A procedure for constructing scattering amplitudes for production processes that is exactly unitary, preserves the bosonic character of the many-particle states, and is invariant with respect to an underlying symmetry group is given. Two simple models, dealing with isospin internal symmetry and the two-dimensional Euclidean space group are presented which illustrate how scattering amplitudes can be represented as matrix elements of groups whose action commutes with the action of the invariance group on the relevant Fock space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01597259
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Polynomial representations of the symplectic groups (1987)
    Springer
    Acta applicandae mathematicae 9 (1987), S. 137-163 
    Details
    ISSN: 1572-9036
    Keywords: 22C35 ; 22E45 ; 22E70 ; 81C40 ; Polynomial representations ; symplectic groups ; Weyl's branching laws ; invariant differentiation inner product
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The irreducible finite dimensional representations of the symplectic groups are realized as polynomials on the irreducible representation spaces of the corresponding general linear groups. It is shown that the number of times an irreducible representation of a maximal symplectic subgroup occurs in a given representation of a symplectic group, is related to the betweenness conditions of representations of the corresponding general linear groups. Using this relation, it is shown how to construct polynomial bases for the irreducible representation spaces of the symplectic groups in which the basis labels come from the representations of the symplectic subgroup chain, and the multiplicity labels come from representations of the odd dimensional general linear groups, as well as from ℂ subgroups. The irreducible representations of Sp(4) are worked out completely, and several examples from Sp(6) are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047536
    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...