Pre-symplectic structure on the space of connections. (English) Zbl 1350.53110

Kori, Tosiaki

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 16th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 6–11, 2014. Sofia: Avangard Prima. 188-194 (2015).

Summary: Let \(X\) be a four-manifold with boundary three-manifold \(M\). We shall describe (i) a pre-symplectic structure on the space \(\mathcal{A}(X)\) of connections on the bundle \(X \times\mathrm{SU}(n)\) that comes from the canonical symplectic structure on the cotangent space \(T ^\ast \mathcal{A}(X)\). By the boundary restriction of this pre-symplectic structure we obtain a pre-symplectic structure on the space \(\mathcal{A}^\flat_0(M)\) of flat connections on \(M \times \mathrm{SU}(n)\) that have null charge.
For the entire collection see [Zbl 1317.00020].

MSC:

53D30	Symplectic structures of moduli spaces
53D50	Geometric quantization
81T50	Anomalies in quantum field theory

Keywords:

pre-symplectic structures; moduli space of flat connections; Chern-Simons functionals