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We extend the well-known notions of a singleton, complete
-set, presheaf and sheaf over a complete Heyting algebra or a right-sided idempotent quantale to arbitrary involutive quantaloids. We show that sheaves on
and complete
-sets come to the same thing. This paper can be considered as a symmetric version of an earlier work of the author. 相似文献
2.
We study solutions of the equations ( - ) = 0 and ( - )2 = 0 in global coordinates on the covering space CAdS
d of the d-dimensional Anti de-Sitter space subject to various boundary conditions and their connection to the unitary irreducible representations of
(d-1,2). The vanishing flux boundary conditions at spatial infinity lead to the standard quantization scheme for CAdS
d in which solutions of the second- and the fourth-order equations are equivalent. To include fields realizing the singleton unitary representation in the bulk of CAdS
d
one has to relax the boundary conditions thus allowing for the nontrivial space of solutions of the dipole equation known as the Gupta–Bleuler triplet. We obtain explicit expressions for the modes of the Gupta–Bleuler triplet and the corresponding two-point function. To avoid negative-energy states one must also introduce an additional constraint in the space of solutions of the dipole equation. 相似文献
3.
There is a chance that singleton fields, that in the context of strings and membranes have been regarded as topological gauge fields that can interact only at the boundary of anti-De Sitter space, at spatial infinity, may have a more physical manifestation as constituents of massless fields in spacetime. The composite character of massless fields is expressed by field-current identities that relate ordinary massless field operators to singleton currents and stress-energy tensors. Naive versions of such identities do not make sense, but when the singletons are described in terms of dipole structures, then such constructions are at least formally possible. The new proposal includes and generalizes an early composite version of QED, and includes quantum gravity, super gravity and models of QCD. Unitarity of such theories is conjectural. 相似文献
4.
Flato Moshé Frønsdal Christian Sternheimer Daniel 《Letters in Mathematical Physics》1999,48(1):109-119
The study starts with the kinematical aspects of singletons and massless particles. It extends to the beginning of a field theory of composite elementary particles and its relations with conformal field theory, including very recent developments and speculations about a possible interpretation of neutrino oscillations and CP violation in this context. This framework was developed during the past twenty years. Based on our deformation philosophy of physical theories, it deals with elementary particles composed of singletons in anti-De Sitter spacetime. 相似文献
5.
R. P. Gylys 《Lithuanian Mathematical Journal》2000,40(2):105-134
We generalize the well-known notions of a singleton, completeQ-set, presheaf, and sheaf over a complete Heyting algebra or a right-sided idempotent quantale to arbitrary quantaloids. We
show that every completeQ-set can be viewed as a sheaf and vice versa.
Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 2, pp. 133–171, April–June, 2000. 相似文献
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