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

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dc.creatorHolender, L.
dc.creatorSantos, M. A.
dc.creatorVancea, I. V.
dc.date2008-01-19
dc.date2008-01-22
dc.date.accessioned2026-07-07T11:39:56Z
dc.date.available2026-07-07T11:39:56Z
dc.descriptionWe 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 $K(z,\bar{z})$ and a real number $λ$. 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 Kähler 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 Kähler 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.
dc.description14 pages, LaTex file. Minor typos corrected
dc.identifierhttps://arxiv.org/abs/0801.3032
dc.identifierhttp://arxiv.org/abs/0801.3032
dc.identifierPhys.Rev.D77:045024,2008
dc.identifierdoi:10.1103/PhysRevD.77.045024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/200103
dc.subjectHigh Energy Physics - Theory
dc.subjectAstrophysics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectFluid Dynamics
dc.titleQuantization of the Relativistic Fluid in Physical Phase Space on Kähler Manifolds
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