Symplectic Yang–Mills theory, Ricci tensor, and connections

Habermann, Katharina; Habermann, Lutz; Rosenthal, Paul

doi:10.1007/s00526-006-0077-2

Cited by 3 publications

(3 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also known are the (Fedosov) * -products for symplectic manifolds endowed with symplectic connections with a nonvanishing associated curvature tensor (see [20,25]). For relatively recent works involving such notions, see for example [29][30][31].…”

Section: Formal Deformations Of Associative Algebras: * -Products And...mentioning

confidence: 99%

Samples of noncommutative products in certain differential equations

Legaré¹

2010

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

A set of associative noncommutative products is considered in different differential equations of the ordinary and partial types. A method of separation of variables is considered for a large set of those systems. The products involved include for example some * products and some products based on Nijenhuis tensors, which are embedded in the differential equations of the Laplace/Poisson, Lax and Schrödinger styles. A comment on the * -products of Reshetikhin-Jambor-Sykora type is also given in relation to * -products of Vey type.

show abstract

Section: Formal Deformations Of Associative Algebras: * -Products And...mentioning

confidence: 99%

Samples of noncommutative products in certain differential equations

Legaré¹

2010

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Many new developments have emerged on symplectic Yang-Mills theories, symplectic Dirac operators and the geometry of Fedosov manifolds. We refer the interested reader to recent [9,10,18].…”

Section: Introductionmentioning

confidence: 99%

On Invariants of Almost Symplectic Connections

Albuquerque

Picken

2015

Math Phys Anal Geom

View full text Add to dashboard Cite

We study the irreducible decomposition under Sp(2n, R) of the space of torsion tensors of almost symplectic connections. Then a description of all symplectic quadratic invariants of torsion-like tensors is given. When applied to a manifold M with an almost symplectic structure, these instruments give preliminary insight for finding a preferred linear almost symplectic connection on M. We rediscover Ph. Tondeur's Theorem on almost symplectic connections. Properties of torsion of the vectorial kind are deduced.

show abstract

“…It is well known that in symplectic geometry there is no analog of the Levi-Civita connection. With the aim to get a deeper insight into the structure of the space of symplectic connections, in [12] an approach of a purely symplectic Yang-Mills theory is given.…”

Section: Introductionmentioning

confidence: 99%