Related papers: Classical-quantum gravity as quantum gravity in di…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
An orthodox formulation of quantum mechanics relies on a set of postulates in Hilbert space supplemented with rules to connect it with classical mechanics such as quantisation techniques, correspondence principle, etc. Here we deduce a…
A discursive, non-technical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such…
The conventional interpretation of quantum mechanics, though it permits a correspondence to classical physics, leaves the exact mechanism of transition unclear. Though this was only of philosophical importance throughout the twentieth…
In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate…
Motivated by quantum gravity, semi-classical theory, and quantum theory on curved spacetimes, we study the system of an oscillator coupled to two spin-1/2 particles. This model provides a prototype for comparing three types of dynamics: the…
Quantum to classical crossover is a fundamental question in dynamics of quantum many-body systems. In frustrated magnets, for example, it is highly non-trivial to describe the crossover from the classical spin liquid with a…
Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is,…
The search for a theory of quantum gravity is the most fundamental problem in all of theoretical physics, but there are as yet no experimental results at all to guide this endeavor. What seems to be needed is a pragmatic way to test if…
A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become…
We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the…
In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…
Quantum gravity is likely the deepest problem facing current physics. While traditionally associated with short distance nonrenormalizability, it is evident that the long distance problem of unitarity, arising at high energies with black…
One of the great challenges for 21st century physics is to quantize gravity and generate a theory that will unify gravity with the other three fundamental forces of nature. This paper takes the (heretical) point of view that gravity may be…