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
Filter
  • 1
    Electronic Resource
    Electronic Resource
    Modular algebras in geometric quantization (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6237-6243 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Presented here is a discussion on the connection between geometric quantization and algebraic quantization. The former procedure relies on a construction of unitary irreducible representations that starts from co-adjoint orbits and uses polarizations, while the latter depends on the purely algebraic characterization of unitary irreducible representations, which is based on central decompositions of von Neumann algebras in involutive duality, and their decompositions in terms of maximal Abelian subalgebras. Intermediate stages of these two quantization methods turn out to be complementary, leading thus to a new characterization of the so-called discrete series representations. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530672
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    On the supersymplectic homogeneous superspace underlying the OSp(1/2) coherent states (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 5951-5963 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this work Onofri and Perelomov's coherent states methods are extended to the recently introduced OSp(1/2) coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely, the OSp(1/2)/U(1) homogeneous superspace, which is clearly identified with a supercoadjoint orbit of OSp(1/2) by exhibiting the corresponding equivariant supermoment map. Moreover, this supermanifold is shown to be a nontrivial example of Rothstein's supersymplectic supermanifolds. More precisely, it is shown that its supersymplectic structure is completely determined in terms of SU(1,1)-invariant (but unrelated) Kähler 2-form and Kähler metric on the unit disc. This result leads to the definition of the notions of a super-Kähler supermanifold and a super-Kähler superpotential, the geometric structure of the former being encoded into the latter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530242
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Geometric quantization of an OSp(1/2) coadjoint orbit (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 13-26 
    Details
    ISSN: 1573-0530
    Keywords: 17A70 ; 32C11 ; 53C55 ; 58A50 ; 58F06 ; 81R05 ; 81S10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In this Letter, we show how the complete geometric quantization extends to specific supersymplectic supermanifolds. More precisely, we extend this procedure to OSp(1/2)-coadjoint orbits, which are graded extensions of elliptic Sp(2, ℝ)-coadjoint orbits. Our approach exploits results obtained in a previous work, where the notion of a super-Kähler supermanifold was defined, and the former orbits were shown to be nontrivial examples of such a notion. As their underlying Kähler manifolds, these supermanifolds carry a natural (super-Kähler) polarization, a crucial notion that was so far lacking. Geometric quantization leads here to a nontrivial representation of osp(1/2), which is realized in a space of square integrable holomorphic sections of a super-Hermitian complex line bundle sheaf-with-connection over the homogenous space OSp(1/2)/U(1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739152
    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...