相关论文: Geometric quantization of generalized oscillator

In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal…

This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…

A new scheme of field quantization is proposed. Instead of associating with different frequencies different oscillators we begin with a single oscillator that can exist in a superposition of different frequencies. The idea is applied to the…

Firstly, we present a reformulation of the standard canonical approach to spherically symmetric systems in which the radial gauge is imposed. This is done via the gauge unfixing technique, which serves as the exposition in the context of…

We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…

In this note we define geometric classical r-matrices and quantum R-matrices, and show how any geometric classical r-matrix can be quantized to a geometric quantum R-matrix. This is one of the simplest nontrivial examples of quantization of…

..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational…

In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.

The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…

The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…

We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…

The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and…

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…

Using the quantum covariant Poisson bracket (QCPB) theory, we can accomplish much more compatible explanations of the quantum mechanics supported by the G-dynamics. We further study the generalized quantum harmonic oscillator equipped with…

The Hamiltonian of the harmonic oscillator is usually defined as a differential operator, but an integral representation can be obtained by using the coherent state quantization. The finite frame quantization is a finite counterpart of the…

States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…

We develop a wave mechanics formalism for qubit geometry using holomorphic functions and Mobius transformations, providing a geometric perspective on quantum computation. This framework extends the standard Hilbert space description,…

We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the…

Extending the methods from our previous work on quantum knots and quantum graphs, we describe a general procedure for quantizing a large class of mathematical structures which includes, for example, knots, graphs, groups, algebraic…

The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise…