相关论文: Quantization and Time

The eigenvalue problem in quantum mechanics is reduced to quantization of the classical action of the physical system. State function of the system, $\psi_0(\phi)$, is written in the form of superposition of two plane waves in the phase…

Preliminaries for Many-Particle approach to quantization of Einstein-Hilbert theory of gravitation are presented in this paper. Einstein-Friedmann Spacetime is detailed discussed from this point of view. Von Neumann-Araki-Woods second…

This article provides an accessible illustration of the measurement approach to the study of the quantum-classical transition suitable for beginning graduate students. As an example, we apply it to a quantum system with a general quadratic…

The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is…

A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…

Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional "supertime", we can dequantize the system in…

In the canonical approach to quantization of gravity, one often uses relational clock variables and an interpretation in terms of conditional probabilities to overcome the problem of time. In this essay we show that these suffer from…

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…

We study the relationship between the quantization of a massless scalar field on the two-dimensional Einstein cylinder and in a spacetime with a time machine. We find that the latter picks out a unique prescription for the state of the zero…

Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…

We consider a quantum test particle in the background of a Newtonian gravitational field in the framework of Cartan's formulation of nonrelativistic spacetimes. We have proposed a novel quantization of a point particle which amounts to…

Canonical quantization applied to closed systems leads to static equations, the Wheeler-deWitt equation in Quantum Gravity and the time independent Schr\"odinger equation in Quantum Mechanics. How to restore time is the Problem of Time(s).…

The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…

In a previous work we have introduced the concept of quasi-integrable quantum system. In the present one we determine sufficient conditions under which, given an integrable classical system, it is possible to construct a quasi-integrable…

We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…

For a particle moving in a one-dimensional space an under a periodic external force, its quantization is study using the Hamiltonian (generalized linear momentum quantization) and constant of motion (velocity quantization) approaches. it is…

This work is a generalization of \cite{baldiotti2021} to Grassmann algebras of arbitrary dimensions. Here we present a covariant quantization scheme for pseudoclassical theories focused on non-hermitian quantum mechanics. The quantization…

The usual quantum mechanics describes the mass eigenstates. To describe the proper-time eigenstates, a duality theory of the usual quantum mechanics was developed. The time interval is treated as an operator on an equal footing with the…

In the paper we consider an interesting possibility of a time as a stochastic process in quantum mechanics.In order to do it we reconsider time as a mechanical quantity in classical mechanics and afterwards we quantize it. We consider…

This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…