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Mathematics > Symplectic Geometry

Title: Pre-symplectic structures on the space of connections

Authors: Tosiaki Kori
Abstract: Let X be a four-manifold with boundary three manifold M. We shall describe (i) a pre-symplectic structure on the space of connections of the trivial SU(n)-bundle over X that comes from the canonical symplectic structure on the cotangent bundle of the connection space, and (ii) a pre-symplectic structure on the space of flat connections of the trivial SU(n)-bundle over M that have null charge. These two structures are related by the boundary restriction map. We discuss also the Hamiltonian feature of the space of connections with the action of the group of gauge transformations.
Comments: 24 pages
Subjects: Symplectic Geometry (math.SG); Mathematical Physics (math-ph)
MSC classes: 53D30, 53D50, 81R10
Cite as: arXiv:1312.4121 [math.SG]
  (or arXiv:1312.4121v4 [math.SG] for this version)

Submission history

From: Toshiaki Kori [view email]
[v1] Sun, 15 Dec 2013 07:50:58 GMT (14kb)
[v2] Wed, 29 Jan 2014 07:04:42 GMT (15kb)
[v3] Sun, 14 Sep 2014 06:05:55 GMT (15kb)
[v4] Thu, 20 Nov 2014 23:27:15 GMT (16kb)