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CLASSICAL FERMI FLUID AND GEOMETRIC ACTION FOR c=1

1993; World Scientific; Volume: 08; Issue: 02 Linguagem: Inglês

10.1142/s0217751x93000138

1793-656X

Avinash Dhar, Gautam Mandal, Spenta R. Wadia,

Physics of Superconductivity and Magnetism

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'.