Related papers: Quantization of the Relativistic Fluid in Physical…
In this paper we address the problem of the quantization of the perfect relativistic fluids formulated in terms of the K\"{a}hler parametrization. This fluid model describes a large set of interesting systems such as the power law energy…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
Let $P$ be a Delzant polytope. We show that the quantization of the corresponding toric manifold $X_{P}$ in toric K\"ahler polarizations and in the toric real polarization are related by analytic continuation of Hamiltonian flows evaluated…
In this paper, we propose a first order action functional for a large class of systems that generalize the relativistic perfect fluids in the K\"{a}hler parametrization to noncommutative spacetimes. We calculate the equations of motion for…
We derive the quantum potential directly from the material derivative of the osmotic velocity and formulate a two-fluid model that reproduces the Madelung equations. Interactions between the fluids are included but remain secondary. The…
In the presence of classical phase space singularities the standard methods are insufficient to attack the problem of quantization.In certain situations the difficulties can be overcome by means of K\"ahler quantization on stratified…
A geometric quantization of a K\"{a}hler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures.…
It has recently been shown that relativistic quantum theory leads to a local interpretation of quantum mechanics wherein the universal wavefunction in configuration space is entirely replaced with an ensemble of local fluid equations in…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
For a very ample line bundle L on a compact connected complex manifold X, with a real structure, we discuss entanglement properties of certain sequences of vectors in tensor products of spaces of holomorphic sections of powers of L.
A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2,R) group manifold. Applied to the cotangent bundle of SL(2,R), the method of Hamiltonian reduction allows us to split the…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kahler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex…
The problem of time is an unsolved issue of canonical General Relativity. A possible solution is the Brown-Kuchar mechanism which couples matter to the gravitational field and recovers a physical, i.e. non vanishing, observable Hamiltonian…
Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…
We derive and analyze a relativistic quantum hydrodynamic (RQHD) system on the Heisenberg group. Starting from the Klein--Gordon--Poisson system, we apply the Madelung transformation to obtain a fluid-type model in which the relativistic…
Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p = \alpha\rho$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered.…
The general relativity theory is redefined equivalently in almost Kahler variables: symplectic form and canonical symplectic connection (distorted from the Levi-Civita connection by a tensor constructed only from metric coefficients and…
A perfect fluid is quantized by the canonical method. The constraints are found and this allows the Dirac brackets to be calculated. Replacing the Dirac brackets with quantum commutators formally quantizes the system. There is a momentum…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…