Related papers: Impenetrable Barriers and Canonical Quantization
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or…
We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations.
The basic features of the complex canonical formulation of general relativity and the recent developments in the quantum gravity program based on it are reviewed. The exposition is intended to be complementary to the review articles…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…
This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…
The notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
Understanding the role of correlations in quantum systems is both a fundamental challenge as well as of high practical relevance for the control of multi-particle quantum systems. Whereas a lot of research has been devoted to study the…
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…
There exists the problem to construct a quantum algebra of observables in lightcone QCD beyond the perturbative regime. It has recently established that the boundary gauge fields are crucial for a consistent construction of the classical…
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…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
A canonical quantization scheme is represented for a quantum system interacting with a nonlinear absorbing environment. The environment is taken anisotropic and the main system is coupled to its environment through some coupling tensors of…
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…
In this paper, we discuss content and context for quantum properties. We give some examples of why quantum properties are problematic: they depend on the context in a non-trivial way. We then connect this difficulty with properties to the…