Quantization of the Relativistic Fluid in Physical Phase Space on Kähler Manifolds

Details Quantization of the Relativistic Fluid in Physical Phase Space on Kähler Manifolds Quantization of the Relativistic Fluid in Physical Phase Space on Kähler Manifolds

2008-01-19

arxiv.org/abs/0801.3032v2

Phys.Rev.D77:045024,2008

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, LaTex file. Minor typos corrected

Scientific paper

10.1103/PhysRevD.77.045024

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 K\"{a}hler manifold, and parametrized by the K\"{a}hler potential $K(z,\bar{z})$ and a real number $\lambda$. In the hamiltonian formulation, the canonical conjugate momenta of the potentials are subjected to second class constraints which allow us to apply the symplectic projector method in order to find the physical degrees of freedom and the physical hamiltonian. We construct the quantum theory for that class of models by employing the canonical quantization methods. We also show that a semiclassical theory in which the K\"{a}hler and the complex potential are not quantized has a highly degenerate vacuum. Also, we define and compute the quantum topological number (quantum linking number) operator which has non-vanishing contributions from the K\"{a}hler and complex potentials only. Finally, we show that the vacuum and the states formed by tensoring the number operators eigenstates have zero linking number and show that linear combinations of the tensored number operators eigenstates which have the form of entangled states have non-zero linking number.

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