Related papers: Quantum Cauchy Surfaces in Canonical Quantum Gravi…
The diffeomorphism symmetry of general relativity leads in the canonical formulation to constraints, which encode the dynamics of the theory. These constraints satisfy a complicated algebra, known as Dirac's hypersurface deformation…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…
The quantum theory of ur objects postulates that all existing physical objects and their properties are constructed from fundamental objects called ur objects being described by an element of a two dimensional complex Hilbert space. This…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
We consider Dolbeault-Dirac operators on quantum projective spaces, following Krahmer and Tucker-Simmons. The main result is an explicit formula for their squares, up to terms in the quantized Levi factor, which can be expressed in terms of…
The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a…
$SU(\infty)-QGR$ is a foundationally quantum approach to cosmology and gravity. It assumes that the Hilbert space of the Universe as a whole represents the symmetry group $SU(\infty)$, and demonstrates this symmetry for Hilbert spaces of…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fact that the quantum theory is based on…
A direct pathway from Hilbert's ``Foundation of Physics'' to Quantum Gravity is established through Dirac's Hamiltonian reduction of General Relativity and Bogoliubov's transformation by analogy with a similar pathway passed by QFT in 20th…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
We apply the reduced phase space quantization to the Kasner universe. We construct the kinematical phase space, find solutions to the Hamilton equations of motion, identify Dirac observables and arrive at physical solutions in terms of…
A consistent quantum theory of gravity has remained elusive ever since the emergence of General Relativity and Quantum Field Theory. Attempts to date have not yielded a candidate that is either free from problematic theoretical…
We prove that a smooth Riemannian manifold admitting an imaginary generalized Killing spinor whose Dirac current satisfies an additional algebraic constraint condition can be embedded as spacelike Cauchy hypersurface in a smooth Lorentzian…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
In this paper, we analyse the well-posedness of the initial value formulation for particular kinds of geometric scalar-tensor theories of gravity, which are based on a Weyl integrable space-time. We will show that, within a frame-invariant…