Related papers: Knot theory and quantum gravity in loop space: a p…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
A key aspect of a recent proposal for a {\em generalized loop representation} of quantum Yang-Mills theory and gravity is considered. Such a representation of the quantum theory has been expected to arise via consideration of a particular…
The philosophy of the Loop Quantum Gravity approach is to construct the canonical variables by using the duality of infinitesimal connections and holonomies along loops. Based on this fundamental property for example the holonomy-flux…
We present an elementary introduction to one of the most important today knot theory approaches, which gives rise to a representation for a class of knot polynomials in terms of quantum groups. Historically, the approach was at the same…
Consider the interior of a black hole or the very early universe: matter is so densely localized that neither the effects of gravity nor those of quantum theory can be ignored. But this entails that neither general relativity nor quantum…
The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is…
In recent work on Einstein gravity in four dimensions using the Ashtekar variables, non-local loop variables have played an important role in attempts to formulate a quantum theory. The introduction of such variables is guided by gauge…
A Newtonian approach to quantum gravity is studied. At least for weak gravitational fields it should be a valid approximation. Such an approach could be used to point out problems and prospects inherent in a more exact theory of quantum…
We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z=3 in the UV. (As in condensed matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short…
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the moyal star product, which enables the representation of the field quantities…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
We show that the exponential of the Gauss (self) linking number of a knot is a solution of the Wheeler-DeWitt equation in loop space with a cosmological constant. Using this fact, it is straightforward to prove that the second coefficient…
The Gauss constraint in the extended loop representation for quantum gravity is studied. It is shown that there exists a sector of the state space that is rigorously gauge invariant without the generic convergence issues of the extended…
It has been argued based on electric-magnetic duality that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four-dimension. And the Euler characteristic of…
Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…
Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short…
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…
These lectures present a general critical assessment of various frameworks for quantum gravity, with particular emphasis on string theory. The topics discussed cover field-theoretical approaches to quantum gravity, anomalies, bosonic and…
These Lecture Notes provide an elementary introduction to the quantization of two-dimensional quantum gravity. Nothing beyond undergratuate physics and mathematic is required. Explicit formulas for the partition functions for universes with…