Related papers: From Loop Quantum Gravity to a Theory of Everythin…
We discuss the action of the configuration operators of loop quantum gravity. In particular, we derive the generalised eigenbasis for the Wilson loop operator and show that the transformation between this basis and the spin-network basis is…
We develop a generalized projective gauge theory of gravity and spinorial matter, incorporating both non-metricity and torsion. The work is divided into three parts. Part I provides a thorough review of General Relativity, Metric-Affine…
Attempts to formulate a quantum theory of gravitation are collectively known as {\it quantum gravity}. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special…
The gravitational interaction, as described by the Einstein-Cartan theory, is shown to emerge as the by-product of the spontaneous symmetry breaking of a gauge symmetry in a pre-geometric four-dimensional spacetime. Starting from a…
We study the algebra of Wilson line operators in three-dimensional N=2 supersymmetric U(M) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M,N), and its connection to K-theoretic Gromov-Witten invariants for Gr(M,N).…
We present the geodesic nature and quantization of geometric shift vector in quantum systems, with the parameter space defined by the Bloch momentum, using the Wilson loop approach. Our analysis extends to include bosonic phonon drag shift…
In the 1960's, Mandelstam proposed a new approach to gauge theories and gravity based on loops. The program for gauge theories was completed for Yang--Mills theories by Gambini and Trias in the 1980's. Gauge theories could be understood as…
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Let us\ann{as} abbreviate the spatial Hamilton functions of the Standard Model by…
As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define…
We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…
This paper develops a framework for the Hamiltonian quantization of complex Chern-Simons theory with gauge group $\mathrm{SL}(2,\mathbb{C})$ at an even level $k\in\mathbb{Z}_+$. Our approach follows the procedure of combinatorial…
Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for…
We present an overview on relational observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a…
Let $\mathfrak{g}$ be a simple Lie algebra. We study 1/2-BPS Wilson loops of supersymmetric 5d $\mathfrak{g}$-type quiver gauge theories on a circle, in a non-trivial instanton background. The Wilson loops are codimension 4 defects of the…
This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…
The Yang-Mills theory associated with the restricted Lorentz group is revisited as a candidate for a theory of gravity. This is a natural idea because the principle of equivalence of gravitation and inertia suggests to introduce locally…
We consider the background-independent quantization of a general scale-invariant theory of gravity with matter, which supports a conserved Weyl current recently suggested as a natural flow of time. For scalar-metric systems, a conformal…
Viewing Einstein's theory as the gauge theory of Lorentz group, we construct the most general vacuum connections which have vanishing curvature tensor and show that the vacuum space-time can be classified by the knot topology…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to…