Related papers: The Unification of Classical and Quantum Gravity
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
Canonical quantization (CQ) is built around $[Q,P]=i\hbar1\!\!1$, while affine quantization (AQ) is built around $[Q,D]=i\hbar\,Q$, where $D\equiv(PQ+QP)/2$. The basic CQ operators must fit $-\infty< P, Q <\infty$, while the basic AQ…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
The mathematical possibility of coupling two quantum dynamic systems having two different Planck constants, respectively, is investigated. It turns out that such canonical dynamics are always irreversible. Semiclassical dynamics is obtained…
There is a long-standing debate about whether gravity should be quantised. A powerful line of argument in favour of quantum gravity considers models of hybrid systems consisting of coupled quantum-classical sectors. The conclusion is that…
The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using…
We give a general overview of various flavors of the equivalence principle in classical and quantum physics, with special emphasis on the so-called weak equivalence principle, and contrast its validity in mechanics versus field theory. We…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
Quantum Gravity by Causal Dynamical Triangulation has over the last few years emerged as a serious contender for a nonperturbative description of the theory. It is a nonperturbative implementation of the sum-over-histories, which relies on…
Gravity does not naturally fit well with canonical quantization. Affine quantization is an alternative procedure that is similar to canonical quantization but may offer a positive result when canonical quantization fails to offer a positive…
String Quantum Gravity is motivated and introduced. Advances in the study of the classical and quantum string dynamics in curved spacetime are reported: 1-New Classes of Exact Multistring solutions in curved spacetimes. 2-Mass spectrum of…
Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity, (ii) a regularized projection operator procedure to accomodate first- and second-class quantum constraints, and (iii) a hard-core interpretation…
The classical-quantum duality at the basis of quantum theory is here extended to the Planck scale domain. The classical/semiclassical gravity (G) domain is dual (in the precise sense of the classical-quantum duality) to the quantum (Q)…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of these: the logic of propositions, symmetry,…
A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems…
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…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants…