Geometric Quantization and Two Dimensional QCD

Details Geometric Quantization and Two Dimensional QCD Geometric Quantization and Two Dimensional QCD

1997-05-14

arxiv.org/abs/hep-th/9705103v1

Commun.Math.Phys. 192 (1998) 493-517

Physics

High Energy Physics

High Energy Physics - Theory

46 pages, Latex, no figures

Scientific paper

10.1007/s002200050306

In this article, we will discuss geometric quantization of 2d QCD with fermionic and bosonic matter fields. We identify the respective large-N_c phase spaces as the infinite dimensional Grassmannian and the infinite dimensional Disc. The Hamiltonians are quadratic functions, and the resulting equations of motion for these classical systems are nonlinear. In a previous publication, the first author has shown that the linearization of the equations of motion for the Grassmannian gave the `t Hooft equation. We will see that the linearization in the bosonic case leads to the scalar analog of the `t Hooft equation found by Tomaras.

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