Related papers: Generalizing the Kodama State I: Construction
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
The canonically quantized 3+1 General Relativity with the global one dimensionality conjecture defines the model, which dimensionally reduced and secondary quantized yields the one-dimensional quantum field theory wherein the generic…
In this paper, I investigate the possible quantization, in the context of LQG, of three dimensional gravity in the case of positive cosmological constant {\Lambda} and try to make contact with alternative quantization approaches already…
We provide a new perspective on the cosmological constant by exploring the background-independent Wheeler-DeWitt quantization of general relativity. The Chern-Simons-Kodama state of quantum gravity, a generalization of the Hartle-Hawking…
We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the…
A noncommutative-geometric generalization of the classical formalism of frame bundles is developed, incorporating into the theory of quantum principal bundles the concept of the Levi-Civita connection. The construction of a natural…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the…
In hep-th/0506040 we discussed a classically constrained model of gravity. This theory contains known solutions of General Relativity (GR), and admits solutions that are absent in GR. Here we study cosmological implications of some of these…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
The aim of the paper is to extend the notion of $\alpha$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these…
Unless the reality of spacetime singularities is assumed, astrophysical black holes cannot be identical to their mathematical counterparts obtained as solutions of the Einstein field equations. Mechanisms for singularity regularization…
Two-dimensional quantum gravity has led to numerous curious results since it was developed in the 1980s. Following the method of the original works, we derive the effective action for the simplest modifications of the theory, when the…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…