arXiv subjects

Charles H-T Wang

Publications and source records attributed to Charles H-T Wang.

3 recordsLinked to original sources

arXiv2018

Quantisation of Paths in Space-Time and Non-Perturbative Quantum Gravity

In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a discrete spacetime and shows that macroscopic spacetime is a renormalization limiting form. Weaving together a number of our previous results we then prove that quantum states invariant under either an external group of local diffeomorphisms of spacetime or by contrast quantum states invariant under the internal action of a compact Lie group are common in a well-defined sense. These form the building blocks of invariant fields and Lagrangians. A form of supersymmetry and noncommutative spacetime naturally emerges, which predicts a massless graviton and its companion gravitino.

gr-qc↗

arXiv2004

Nonlinear quantum gravity on the constant mean curvature foliation

A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analyzed as nonlinear quantum minisuperspaces in the context of the proposed theory.

gr-qc↗

arXiv2004

An action principle for the quantization of parametric theories and nonlinear quantum cosmology

By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to nonlinear quantum mechanics. This generalization enables a unitary description of the quantum evolution for a broad class of constrained Hamiltonian systems with a nonlinear kinematic structure. In particular, the new theory is applicable to the quantization of cosmological models where a chosen gravitational degree of freedom acts as geometric time. This is demonstrated explicitly using three cosmological models: the Friedmann universe with a massless scalar field and Bianchi type I and IX models. Based on these investigations, the prospect of further developing the proposed quantization scheme in the context of quantum gravity is discussed.

gr-qc↗