Proceedings of the International Conference on Geometry, Integrability and Quantization

Classical Mechanics on Grassmannian and Disc

A. Konechny, S. G. Rajeev, and O. T. Turgut

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

Source
Proceedings of the Second International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2001), 181-207

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


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