Related papers: Quantum Cauchy Surfaces in Canonical Quantum Gravi…
We construct generalized quantum Cauchy pre-measures that correspond to the analytic continuation of the transition probability of the Cauchy process to imaginary time. We show that these complex pre-measures of time translations extend to…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
We propose a model of quantum gravity in arbitrary dimensions defined in terms of the BV quantization of a supersymmetric, infinite dimensional matrix model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the space of…
Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint…
In our model of quantum gravity the quantum development of a Cauchy hypersurface is governed by a wave equation derived as the result of a canonical quantization process. To find physically interesting solutions of the wave equation we…
For particles constrained on a curved surface, how to perform quantization within Dirac's canonical quantization scheme is a long-standing problem. On one hand, Dirac stressed that the Cartesian coordinate system has fundamental importance…
Curvature is a key notion in General Relativity, characterizing the local physical properties of spacetime. By contrast, the concept of curvature has received scant attention in nonperturbative quantum gravity. One may even wonder whether…
We quantize spherically symmetric electrovacuum gravity. The algebra of Hamiltonian constraints can be made Abelian via a rescaling and linear combination with the diffeomorphism constraint. As a result the constraint algebra is a true Lie…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…
Canonical vacuum gravity is expressed in generally-covariant form in order that spacetime diffeomorphisms be represented within its equal-time phase space. In accordance with the principle of general covariance, the time mapping ${\T}:…
We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and…
Here we will consider examples of conformally flat manifolds that are conformally equivalent to open subsets of the n-dimensional sphere. For such manifolds we shall introduce a Cauchy kernel and Cauchy integral formula for sections tasking…
We develop a ``canonical Wick rotation-rescaling theory in 3-dimensional gravity''. This includes: (a) A simultaneous classification that shows how generic maximal globally hyperbolic spacetimes of constant curvature, which admit a complete…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…
Building on the results of previous work, we demonstrate how matter fields are incorporated into the general linear frame approach to general relativity. When considering the Maxwell one-form field, we find that the system that leads…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…