
We present a conformal theory of a dissipationless relativistic fluid in 2 space-time dimensions. The theory carries with it a representation of the algebra of 2-$D$ area-preserving diffeomorphisms in the target space of the complex scalar potentials. A complete canonical description is given, and the central charge of the current algebra is calculated. The passage to the quantum theory is discussed in some detail; as a result of operator ordering problems, full quantization at the level of the fields is as yet an open problem.
17 pages, no figures
Analogues of general relativity in lower dimensions, Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems, Quantum hydrodynamics and relativistic hydrodynamics, High Energy Physics - Theory, High Energy Physics - Theory (hep-th), FOS: Physical sciences, Methods of quantum field theory in general relativity and gravitational theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
Analogues of general relativity in lower dimensions, Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems, Quantum hydrodynamics and relativistic hydrodynamics, High Energy Physics - Theory, High Energy Physics - Theory (hep-th), FOS: Physical sciences, Methods of quantum field theory in general relativity and gravitational theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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