Related papers: Metrical Quantization
The quantum mechanical measurement problem does not arise in the quantum real number approach to quantum measurements of the first kind. The attributes of individual microscopic systems in the experimental ensemble always have qr-number…
Quantization of general relativity in metric variables using ``precanonical'' quantization based on the De Donder-Weyl covariant Hamiltonian formulation is outlined. Elements of classical geometry needed to formulate the (Dirac-like) wave…
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
New features of a previously introduced Group Approach to Quantization are presented. We show that the construction of the symmetry group associated with the system to be quantized (the "quantizing group") does not require, in general, the…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
In accordance with the fact that quantum measurements are described in terms of positive operator measures (POMs), we consider certain aspects of a quantization scheme in which a classical variable $f:\R^2\to \R$ is associated with a unique…
We have quantized a flat cosmological model in the context of the metric f(R) models, using the causal Bohmian quantum theory. The equations are solved and then we have obtained how the quantum corrections influence the classical equations.
Quantum phenomena offer the possibility of measuring physical quantities with precision beyond classical limits. However, current progress is constrained by scalability, environmental noise, and challenges in practical integration. This…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
We will give a new model for measurements of a quantum system such that the measuring apparatuses are described by a unital separable non-type I nuclear simple C$^*$-algebra equipped with certain unital endomorphisms and pure states. An…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
We discuss the canonical quantization of systems formulated on discrete space-times. We start by analyzing the quantization of simple mechanical systems with discrete time. The quantization becomes challenging when the systems have…
In this work, we study the quantization of Carrollian conformal scalar theories, including two-dimensional(2D) magnetic scalar and three-dimensional(3D) electric and magnetic scalars. We discuss two different quantization schemes, depending…
In ordinary Quantum Mechanics only ideally instantaneous observations of a quantity or a set of compatible quantities are usually considered. In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of…
The recently introduced framework of Graded Quantitative Rewriting is an innovative extension of traditional rewriting systems, in which rules are annotated with degrees drawn from a quantale. This framework provides a robust foundation for…
A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is…
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and…