scholarly journals Geometric viewpoint on the quantization of a fuzzy logic

2020 ◽  
Vol 17 (13) ◽  
pp. 2050201
Author(s):  
Davide Pastorello
Keyword(s):  
Fuzzy Logic ◽  
Phase Space ◽  
Complex Projective Space ◽  
Product Formula ◽  
Kähler Structure ◽  
Set Operations ◽  
Logical Connectives ◽  
Standard Set ◽  
Complex Projective ◽  
Geometric Formulation

Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel [Formula: see text]-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations. Considering the geometric formulation of quantum mechanics we give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with Kähler structure (the quantum phase space) obtaining a quantized version of a fuzzy logic by deformation of the product [Formula: see text]-norm.

scholarly journals Noncompact CPN as a phase space of superintegrable systems

2021 ◽  
Vol 36 (08n09) ◽  
pp. 2150055
Author(s):  
Erik Khastyan ◽  
Armen Nersessian ◽  
Hovhannes Shmavonyan
Keyword(s):  
Phase Space ◽  
Complex Projective Space ◽  
Coulomb Systems ◽  
Kähler Structure ◽  
Higher Dimensional ◽  
Superintegrable Systems ◽  
Constants Of Motion ◽  
Complex Projective ◽  
Klein Model

We propose the description of superintegrable models with dynamical [Formula: see text] symmetry, and of the generic superintegrable deformations of oscillator and Coulomb systems in terms of higher-dimensional Klein model (the noncompact analog of complex projective space) playing the role of phase space. We present the expressions of the constants of motion of these systems via Killing potentials defining the [Formula: see text] isometries of the Kähler structure.

scholarly journals ACTION ANGLE VARIABLES FOR COMPLEX PROJECTIVE SPACE AND SEMICLASSICAL EXACTNESS

1994 ◽  
Vol 09 (36) ◽  
pp. 3339-3346 ◽  
Author(s):  
PHILLIAL OH ◽  
MYUNG-HO KIM
Keyword(s):  
Phase Space ◽  
Complex Projective Space ◽  
Integrable Model ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Phase Approximation ◽  
Path Integral Representation ◽  
Complex Projective ◽  
Classical Integrable ◽  
State Path

We construct the action angle variables of a classical integrable model defined on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase approximation. We show that the resulting expression for the propagator coincides with the exact propagator which was obtained by solving the time-dependent Schrödinger equation.

scholarly journals A geometrization of quantum mutual information

2019 ◽  
Vol 17 (02) ◽  
pp. 1950011
Author(s):  
Davide Pastorello
Keyword(s):  
Quantum Mechanics ◽  
Mutual Information ◽  
Projective Space ◽  
Quantum System ◽  
Complex Projective Space ◽  
Geometric Description ◽  
Composite Quantum System ◽  
Quantum Mutual Information ◽  
Complex Projective ◽  
Geometric Formulation

It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kähler manifold. In this paper, we consider the notion of mutual information among continuous random variables in relation to the geometric description of a composite quantum system introducing a new measure of total correlations that can be computed in terms of Gaussian integrals.

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

Reduction theorem of the codimension of minimal generic submanifolds in a complex projective space

1995 ◽  
Vol 54 (2) ◽  
pp. 137-143
Author(s):  
Sung-Baik Lee ◽  
Seung-Gook Han ◽  
Nam-Gil Kim ◽  
Masahiro Kon
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Reduction Theorem ◽  
Generic Submanifolds ◽  
Complex Projective
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