ar X iv : 0 70 9 . 21 70 v 2 [ he p - th ] 1 3 N ov 2 00 7 Quantization of the Relativistic Fluid in Physical Phase Space on Kähler Manifolds

We discuss the quantization of a class of relativistic fluid models defined in terms of one real and two complex conjugate potentials with values on a Kähler manifold and parametrized by the Kähler potential K(z, z) and a real number λ. The fluid potential fields represent the degrees of freedom of the system while the conserved currents are responsible for the topological charges. In the hamiltonian formulation, the canonical conjugate momenta of the potentials are subjected to second class constraints. The physical degrees of freedom and the physical hamiltonian are obtained by applying the symplectic projector constructed from the Dirac and the symplectic matrices. We apply the canonical quantization method to the canonical conjugate fields θ and πθ as well as to the vector potential field A(K, z, z) constructed from the Kähler potential and the fluid complex potentials. The one-particle excitations of the fluid potential fields are discussed. We show that the quantum relativistic fluid has a vanishing linking number operator. The semiclassical quantization in which the vector potential A(K, z, z) is kept classical while the canonical conjugate fields are quantized is also discussed. email: [email protected] email: [email protected] email: [email protected]