Related papers: Minimal Length, Measurability and Gravity
The effects of a minimal length are investigated within an algebraically extended theory of General Relativity (GR). Former attempts, to include a minimal length in GR are first resumed, with a conformal factor of the metric as a…
This paper discusses the somewhat unintuitive conjecture that many Lorentz-invariant many-particle models can be reinterpreted to satisfy the gtr field equations. It is shown that a careful remapping of coordinates yields a non-trivial…
Quantum electrodynamics is the well-accepted theory. However, we feel it is useful to look at formalisms that provide alternative ways to describe light, because in the recent years the development of quantum field theories based primarily…
We extend the classical general relativistic theory of measurement to include the possibility of existence of higher dimensions. The intrusion of these dimensions in the spacetime interval implies that the inertial mass of a particle in…
An approach to the quantization of gravity in the presence matter is examined which starts from the classical Einstein-Hilbert action and matter approximated by "point" particles minimally coupled to the metric. Upon quantization, the…
Magnitude is an isometric invariant of metric spaces introduced by Leinster. Since its inception, it has inspired active research into its connections with integral geometry, geometric measure theory, fractal dimensions, persistent…
In the vast amount of results linking gravity with thermodynamics, statistics, information, a path is described which tries to explore this connection from the point of view of (non)locality of the gravitational field. First the emphasis is…
First, we briefly review the description of gravity theories as gauge theories in three and four dimensions. Specifically, we recall the procedure in which the results of General Relativity in three and four dimensions are recovered in a…
Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field…
A very brief review is given of the current state of research in quantum gravity. Over the past fifteen years, two approaches have emerged as the most promising paths to a quantum theory of gravity: string theory and quantum geometry. I…
We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General Relativity cannot be quantized -- unless it is…
Quantum gravity is the missing piece in our understanding of the fundamental interactions today. Given recent observational breakthroughs in gravity, providing a quantum theory for what lies beyond general relativity is more urgent than…
We show that the metric (line element) is the first geometrical object to be associated to a discrete (quantum) structure of the spacetime without necessity of black hole-entropy-area arguments, in sharp contrast with other attempts in the…
A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for…
General relativity postulates that the gravity field is defined on a Riemannian manifold. The field equations are $R^\mu_\nu = 0$ i.e. Ricci's curvature tensor vanishes. The field equations have to be augmented by natural physical…
One of the leading candidates for quantum gravity, viz. string theory, has the following features incorporated in it. (i) The full spacetime is higher dimensional, with (possibly) compact extra-dimensions; (ii) There is a natural minimal…
Investigating quantum gravity requires a comprehension of both, general relativity and quantum field theory. Therefore this thesis starts, after a general introduction to the treated topics, with a brief review of the field theoretical…
Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…
A possible way out of the conundrum of quantum gravity is the proposal that general relativity (GR) is not a fundamental theory but emerges from an underlying microscopic description. Despite recent interest in the emergent gravity program…