ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

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
    The character of the exceptional series of representations of SU(1,1) (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 461-467 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The character of the exceptional series of representations of SU(1,1) is determined by using Bargmann's realization of the representation in the Hilbert space Hσ of functions defined on the unit circle. The construction of the integral kernel of the group ring turns out to be especially involved because of the nonlocal metric appearing in the scalar product with respect to which the representations are unitary. Since the nonlocal metric disappears in the "momentum space," i.e., in the space of the Fourier coefficients the integral kernel is constructed in the momentum space, which is transformed back to yield the integral kernel of the group ring in Hσ. The rest of the procedure is parallel to that for the principal series treated in a previous paper. The main advantage of this method is that the entire analysis can be carried out within the canonical framework of Bargmann. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533149
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The Clebsch–Gordan problem of the SL(2,R) coherent states (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3826-3835 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Clebsch–Gordan problems of the Barut–Girardello, and Perelomov coherent states of SL(2,R) are studied using the associated Hilbert spaces as the respective carrier spaces of the representations of the group. For the Barut–Girardello coherent states this Hilbert space is a subspace of the Bargmann–Segal Hilbert space B(C2) called the "reduced Bargmann space.'' The generators of the group in this realization are essentially the boson operators of Holman and Biedenharn which provide a convenient starting point of the problem. For the Perelomov coherent states the associated Hilbert space turns out to be Bargmann's canonical carrier space for the realization of the discrete series of representations, namely, the Hilbert space of functions analytic inside the open unit disc. The scalar product, the principal vector, and a complete orthonormal set in these Hilbert spaces are constructed and used for the explicit evaluation of the Clebsch–Gordan coefficients. For each of the coherent state systems the product state turns out to be the principal vector and, therefore, the coupled state itself is the Clebsch–Gordan coefficient. For the Barut–Girardello coherent states this is, apart from normalization, the product of a Bessel function and d-function. For the Perelomov coherent states, on the other hand, this closely resembles the Clebsch–Gordan coefficient of the SU(2) coherent states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529880
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Representations of SL(2,R) in a Hilbert space of analytic functions and a class of associated integral transforms (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1-8 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the boson operators of SL(2,R) realized as hyperdifferential operators in Bargmann's Hilbert space of analytic functions yield, on exponentiation, a parametrized continuum of integral transforms. Each value of the group parameters yields an integral transform pair. For the metaplectic representation the resulting integral transform is essentially the mapping of the Moshinsky–Quesne transform in Bargmann's Hilbert space B(C). The formula for the inversion of this transform is obtained simply by replacing the group element by its inverse. The corresponding Hilbert space for arbitrary representations of the discrete series is B(C2), where C2 is the two-dimensional complex Euclidean space. To carry out the reduction of B(C2) into the eigenspaces Bk(C) (k= 1/2 ,1, (3)/(2) ,...) of irreducible representations of the positive discrete class, the complex polar coordinates (z1=z cos φ, z2=z sin φ) in C2 are introduced. The "reduced Bargmann space'' Bk(C) has many interesting features. The elements of Bk(C) are entire functions of the complex "radius'' z analytic in the upper half-plane. In contrast to the Gaussian measure in B(C2), the integration measure in the scalar product in Bk(C) contains a modified Bessel function of the second kind. The principal vector in Bk(C), on the other hand, is a modified Bessel function of the first kind. The resulting integral transform maps Bk(C) onto itself and the integral kernel is the product of an exponential and a modified Bessel function of the first kind. The inversion formula for this transform is obtained again by replacing the group element by its inverse.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528571
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    The mannitol cycle in Pleurotus ostreatus (Florida) (2004)
    Oxford, UK : Blackwell Publishing Ltd
    FEMS microbiology letters 236 (2004), S. 0 
    Details
    ISSN: 1574-6968
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Biology
    Notes: In mushroom, presence of the mannitol cycle has not been reported so far although the polyol is supposed to be generated by the reduction of fructose by mannitol dehydrogenase. This study submits evidence for the presence of the mannitol cycle in Pleurotus ostreatus. The key enzyme of the cycle, mannitol-1-phosphate dehydrogenase (M1PDH), was present appreciably in all the developmental stages of the mushroom. However, the enzyme level dropped significantly at the onset of sporulation. The presence of M1DPH was confirmed by isozyme analysis and RT-PCR mediated amplification of a ∼400 bp DNA fragment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1574-6968.2004.tb09662.x
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    The Gel'fand realization and the generating function of the Clebsch–Gordan coefficients of SL(2,R) in the hyperbolic basis (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 514-519 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the canonical realization of the representations of SL(2,R) proposed by Gel'fand and co-workers yields a generating function of the Clebsch–Gordan coefficients of the group in the hyperbolic basis. This function is the coupled state and appears as the solution of an ordinary differential equation reducible to the hypergeometric equation. The desired expansion of the generating function that yields the Clebsch–Gordan coefficients is essentially a generalization of Barnes' theory of analytic continuation of the hypergeometric function. In this paper the normalized Clebsch–Gordan coefficients for the coupling of two representations of the positive discrete class are calculated. The final result is an analytic continuation of the corresponding expression in the SO(2) basis. The possible application of the generating function to the reduction of the Kronecker product of three irreducible representations is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527827
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    The Gel'fand realization and the exceptional representations of SL(2,R) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 12-17 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the canonical representation space of Gel'fand and co-workers is particularly appropriate for problems requiring explicit reduction under the noncompact SO(1,1) and E(1) bases for both the principal and exceptional series of representations of SL(2,R). We use this realization to set up complete orthonormal sets of eigendistributions corresponding to the three subgroup reductions, namely, SL(2,R)&supuline;SO(1,1), SL(2,R)&supuline;E(1), and SL(2,R)&supuline;SO(2), and evaluate the unitary transformations connecting these reductions. These overlap matrix elements appear as the applications of these distributions to a set of well-defined test functions. Using the rigorous theory of analytic continuation we show that the results for the exceptional representations have the same analytic forms as the corresponding results for the principal series. Some of these results are essential prerequisites for the solution of the Clebsch–Gordan problem (series and coefficients) of SL(2,R) in the SO(1,1) basis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526799
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Hilbert spaces of analytic functions for the SL(2,R) coherent states and a class of associated integral transforms (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3612-3623 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the Bargmann–Segal Hilbert spaces of entire analytic functions and Bargmann's canonical Hilbert spaces of functions analytic within the open unit disc are connected by simple integral transform pairs. A further consequence of this analysis is the analog of the Bargmann transform for the SL(2,R) [or SU(1,1)] group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530434
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    A unified treatment of the characters of SU(2) and SU(1,1) (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3209-3229 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The character problems of SU(2) and SU(1,1) are re-examined from the standpoint of a physicist by employing the Hilbert space method which is shown to yield a completely unified treatment for SU(2) and the discrete series of representations of SU(1,1). For both the groups the problem is reduced to the evaluation of an integral which is invariant under rotation for SU(2) and Lorentz transformation for SU(1,1). The integrals are accordingly evaluated by applying a rotation to a unit position vector in SU(2) and a Lorentz transformation to a unit SO(2,1) vector which is time-like for the elliptic elements and space-like for the hyperbolic elements in SU(1,1). The details of the procedure for the principal series of representations of SU(1,1) differ substantially from those of the discrete series. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532042
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    The Barut–Girardello coherent states (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 114-121 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the completeness problem of the SL(2,R) coherent states proposed by Barut and Girardello leads to a moment problem, not a Mellin transform. This moment problem, which also appears in the theory of para-Bose oscillators, has been solved following the Sharma–Mehta–Mukunda–Sudarshan solution of the problem. The matrix element of finite transformation in the coherent state basis is shown to satisfy a "quasiorthogonality'' condition analogous to the orthogonality condition of the matrix element in the canonical basis. Finally, the Barut–Girardello "Hilbert space of entire analytic functions of growth (1,1)'' turns out to be only a subspace of Bargmann's well-known Hilbert space of analytic functions. This subspace, which has been called "the reduced Bargmann space'' in a previous paper, is an invariant subspace of SL(2,R). With this identification the generators of the group in this realization turn out to be the well-known boson operators of Holman and Biedenharn.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529951
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    A class of integral transforms associated with the Majorana representation of SL(2,C) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2035-2039 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the boson operators for the Majorana representation of SL(2,C) realized as hyperdifferential operators in the Bargmann Hilbert space of analytic functions yield, on exponentiation, a parametrized continuum of integral transforms. Each value of the group parameters yields an integral transform pair. The formula for the inversion of the transform is obtained simply by replacing the group element by its inverse.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528653
    Location Call Number Expected 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...