Related papers: Quantization of Nonstandard Hamiltonian Systems
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
Large-N field systems are considered from an unusual point of view. The Hamiltonian is presented in a third-quantized form analogously to the second-quantized formulation of the quantum theory of many particles. The semiclassical…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…
In this paper we introduce the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group…
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
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…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…
It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
The reduced SL(2,R) WZW quantum mechanics is analysed in the framework of geometric quantization. The spectrum of the Hamiltonian is determined, and it is found, that contrary to the previous approaches, there is a unique, physically…
It is argued that the massive non-Abelian gauge field theory without involving Higgs bosons may be well established on the basis of gauge-invariance principle because the dynamics of the field is gauge-invariant in the physical space…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
In a previous work we have introduced the concept of quasi-integrable quantum system. In the present one we determine sufficient conditions under which, given an integrable classical system, it is possible to construct a quasi-integrable…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space C, but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a…
Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum…
One of the central problems in quantum theory is to characterize, detect, and quantify quantumness in terms of classical strategies. Dephasing processes, caused by non-dissipative information exchange between quantum systems and…