Related papers: Quantization of the sphere with coherent states
In this paper we study the quantum phase properties of {\it "nonlinear coherent states"} and {\it "solvable quantum systems with discrete spectra"} using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be…
We propose generalized quantization axioms for Nambu-Poisson manifolds, which allow for a geometric interpretation of n-Lie algebras and their enveloping algebras. We illustrate these axioms by describing extensions of Berezin-Toeplitz…
In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systematic treatment of the construction of such systems and to…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
We introduce a geometric quantification of quantum coherence in single-mode Gaussian states and we investigate the behavior of distance measures as functions of different physical parameters. In the case of squeezed thermal states, we…
The quantization of systems with first- and second-class constraints within the coherent-state path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so…
Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems…
The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced…
Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups.…
This work describes coherent states for a physical system governed by a Hamiltonian operator, in two dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential. The…
In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are…
Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate…
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,…
It has recently been argued that the inability to measure the absolute phase of an electromagnetic field prohibits the representation of a laser's output as a quantum optical coherent state. This argument has generally been considered…