## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Classical Mechanics on Grassmannian and Disc

#### Abstract

In these notes, we will discuss from a purely geometric point of view classical mechanics on certain type of Grassmannians and discs. We will briefly discuss a superversion which in some sense combines these two models, and corresponds to the large-$N_c$ limit of $SU(N_c)$ gauge theory with fermionic and bosonic matter fields, both in the fundamental representation, in $1 + 1$ dimensions [12]. This result is a natural extension of ideas in [16]. There it has been shown that the large-$N_c$ phase space of $1+1$ dimensional QCD is given by an infinite dimensional Grassmannian. The complex scalar field version of this theory is worked out in [18] and it is shown that the phase space is an infinite dimensional disc.

#### Article information

Dates
First available in Project Euclid: 5 June 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1433528473

Digital Object Identifier
doi:10.7546/giq-2-2001-181-207

Mathematical Reviews number (MathSciNet)
MR1815639

Zentralblatt MATH identifier
1062.37051

#### Citation

Konechny, A.; Rajeev, S. G.; Turgut, O. T. Classical Mechanics on Grassmannian and Disc. Proceedings of the Second International Conference on Geometry, Integrability and Quantization, 181--207, Coral Press Scientific Publishing, Sofia, Bulgaria, 2001. doi:10.7546/giq-2-2001-181-207. https://projecteuclid.org/euclid.pgiq/1433528473