Related papers: Metrical Quantization
Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…
The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization {\bf Assumption} and an accompanying {\bf Requirement} is put forward,…
The generalized Einstein action is treated quantum mechanically by using a quadratic lagrangian form. The canonical quantization of this action is obtained by using the auxiliary variable to define the generalized momentum. Physical…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
A series of successive quantizations is considered, starting with the quantization of a non relativistic or relativistic point particle: 1) quantization of a particle's position, 2) quantization of wave function, 3) quantization of wave…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space $\left(x,k\right)$ into Hilbertian operators. The…
We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…
This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the…
The role of the QCD theta-parameter is investigated in pure Yang-Mills theory in the spacetime given by the four-dimensional Euclidean torus. While in this setting the introduction of possibly unphysical boundary conditions is avoided, it…
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
A concept of the generalized quantum measurement is introduced as the transformation, which establishes a correspondence between the initial states of the object system and final states of the object--measuring device (meter) system with…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is…
We study the canonical and the coherent state quantization of a particle moving in a magnetic field on a non-commutative plane. Starting from the so called \theta-modified action, we perform the canonical quantization and analyze the gauge…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…