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Symplectic vector space

About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.


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TL;DR: In this paper, a formulation of the coupling of vector multiplets to N = 2 supergravity which is symplectic covariant (and thus is not based on a prepotential) and uses superconformal tensor calculus is presented.
Abstract: We present a formulation of the coupling of vector multiplets to N = 2 supergravity which is symplectic covariant (and thus is not based on a prepotential) and uses superconformal tensor calculus. We do not start from an action, but from the combination of the generalized Bianchi identities of the vector multiplets in superspace, a symplectic definition of special Kahler geometry, and the supersymmetric partners of the corresponding constraints. These involve the breaking to super-Poincare symmetry, and lead to on-shell vector multiplets. This symplectic approach gives the framework to formulate vector multiplet couplings using a weaker defining constraint for special Kahler geometry, which is an extension of older definitions of special Kahler manifolds for some cases with only one vector multiplet.

8 citations

Journal ArticleDOI
TL;DR: In the non-arguesian setting, any equivalence of nonarguesians and non-symmetric spreads preserves the resulting symplectic structures over the kernels as discussed by the authors.
Abstract: Every nondesarguesian symplectic spread is also symplectic over its kernel. Any equivalence of nondesarguesian symplectic spreads preserves the resulting symplectic structures over the kernels.

8 citations

Journal ArticleDOI
TL;DR: In this paper, a form of the chiral equation for which first integrals can be written explicitly is considered, and a symplectic structure, the Lagrangian and first integral in involution, is found.
Abstract: We deal with a form of the chiral equation, for which first integrals can be written explicitly. For these equations, we find a symplectic structure, the Lagrangian and first integrals in involution.

8 citations

Journal ArticleDOI
TL;DR: Bieliavsky et al. as mentioned in this paper present a short survey of recent work on Ricci-flat symplectic connections, including a moment map for the action of the group of symplectomorphisms on the space of symplectic connection, algebraic construction of a large class of Ricciflat symmetric symplectic spaces, and an example of global reduction in a non-symmetric case.
Abstract: This note contains a short survey on some recent work on symplectic connections: properties and models for symplectic connections whose curvature is determined by the Ricci tensor, and a procedure to build examples of Ricci-flat connections. For a more extensive survey, see Bieliavsky et al. [Int. J. Geom. Methods Mod. Phys. 3, 375–420 2006]. This note also includes a moment map for the action of the group of symplectomorphisms on the space of symplectic connections, an algebraic construction of a large class of Ricci-flat symmetric symplectic spaces, and an example of global reduction in a non-symmetric case.

8 citations

Journal ArticleDOI
TL;DR: In this article, a list of all symplectic 3-symmetric manifolds with simple groups of transvections is given, and a method of constructing semisimple (noncompact) symplectic k-sysmmetric spaces from a given (compact)-Kahler k-space.
Abstract: Bieliavsky introduced and investigated a class of symplectic symmetric spaces, that is, symmetric spaces endowed with a symplectic structure invariant with respect to symmetries. The theory of symmetric spaces has essential and interesting generalizations due to the fundamental work of Gray and Wolf continued by many researchers. Therefore, we ask a question about possible symplectic versions of such theory. In this paper we do obtain such generalization, and, in particular, give a list of all symplectic 3-symmetric manifolds with simple groups of transvections. We also show a method of constructing semisimple (noncompact) symplectic \(k\)-symmetric spaces from a given (compact) Kahler k-symmetric space.

8 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202310
202221
202113
20208
201910
201818