Related papers: Classical and Quantum Gravity in 1+1 Dimensions, P…
We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM$_{1+1}$) by operator-algebraic methods. The latter are based on Hamiltonian lattice gauge theory and multi-scale analysis via inductive…
Integrable models of 1+1 dimensional gravity coupled to scalar and vector fields are briefly reviewed. A new class of integrable models with nonminimal coupling to scalar fields is constructed and discussed.
These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants…
We study some two-dimensional dilaton gravity models using the formal theory of partial differential equations. This allows us to prove that the reduced phase space is two-dimensional without an explicit construction. By using a convenient…
It is well known that by using the infinite dimensional symmetries that issue from string theories, one can build 2D geometric field theories. These 2D field theories can be identified with gravitational and gauge anomalies that arise in…
We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives and…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
As it is well known, the global structure of the Einstein equations for general relativity in the context of the initial value problem, is a difficult and intricate mathematical problem. Therefore, any additional structure in their…
Recently, gauge field theory approaches were extensively used in order to discuss the physical consequences of spin-orbit interactions in condensed matter physics. An SU(2)$\times$U(1) gauge theory is very naturally borne out and provides…
Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging $T(4) \times [SU(3)]_{color} $ in flat space-time, we have a unified…
We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang-Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind…
We do not yet know how to quantize gravity in 3+1 dimensions, but in lower dimensions we face the opposite problem: many of the approaches originally developed for (3+1)-dimensional gravity can be successfully implemented in 2+1 dimensions,…
We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory…
Path integral quantization of generic two-dimensional dilaton gravity non-minimally coupled to a Dirac fermion is performed. After integrating out geometry exactly, perturbation theory is employed in the matter sector to derive the lowest…
The recently developed worldline quantum field theory (WQFT) formalism for the classical gravitational scattering of massive bodies is extended to massive, charged point particles coupling to bi-adjoint scalar field theory, Yang-Mills…
We discuss Weyl (conformal) transformations in two-dimensional matterless dilaton gravity. We argue that both classical and quantum dilaton gravity theories are invariant under Weyl transformations.
By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance,…
We study point particles in 2+1 dimensional first order gravity using a triangulation to fix the connection and frame-field. The Hamiltonian is reduced to a boundary term which yields the total mass. The triangulation is dynamical with…
Nowadays it is widely accepted that the evolution of the universe was driven by some scalar degrees of freedom both on its early stage and at present. The corresponding cosmological models often involve some scalar fields introduced ad hoc.…
We provide a set of exact solutions of the classical Yang-Mills equations. They have the property to satisfy a massive dispersion relation and hold in all gauges. These solutions can be used to describe the vacuum of the quantum Yang-Mills…