Classical Fermi Fluid and Geometric Action for $c=1$

Details Classical Fermi Fluid and Geometric Action for $c=1$ Classical Fermi Fluid and Geometric Action for $c=1$

1992-04-10

arxiv.org/abs/hep-th/9204028v2

Int.J.Mod.Phys.A8:325-350,1993

Physics

High Energy Physics

High Energy Physics - Theory

31 pages. (Revised version)

Scientific paper

10.1142/S0217751X93000138

We formulate the $c=1$ matrix model as a quantum fluid and discuss its classical limit in detail, emphasizing the $\hbar$ corrections. We view the fermi fluid profiles as elements of \winf-coadjoint orbit and write down a geometric action for the classical phase space. In the specific representation of fluid profiles as `strings' the action is written in a four-dimensional form in terms of gauge fields built out of the embedding of the `string' in the phase plane. We show that the collective field action can be derived from the above action provided one restricts to quadratic fluid profiles and ignores the dynamics of their `turning points'.

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