相关论文: Light Cone $W_n$ Geometry and its Symmetries and P…
The BRST anomaly which may be present in the induced $W_n$ gravity quantized on the light-cone is evaluated in the geometrical framework of Zucchini. The cocycles linked by the cohomology of the BRST operator to the anomaly are…
We relate the Teichmuller spaces obtained by Hitchin to the Teichmuller spaces of $WA_{n}$-gravity. The relationship of this space to $W$-gravity is obtained by identifying the flat $PSL(n+1,{\BR})$ connections of Hitchin to generalised…
When joined the unified gauge picture of fundamental interactions, the gravitation theory leads to geometry of a space-time which is far from simplicity of pseudo-Riemannian geometry of Einstein's General Relativity. This is geometry of the…
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation…
A geometrical study of supergravity defined on (1|1) complex superspace is presented. This approach is based on the introduction of generalized superprojective structures extending the notions of super Riemann geometry to a kind of super…
In the paper "Is there a Jordan geometry underlying quantum physics?" (Int. J. Theor. Phys., to appear; arXiv:0801.3069 [math-ph]), generalized projective geometries have been proposed as a framework for a geometric formulation of Quantum…
The higher-spin geometries of $W_\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic…
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…
We discuss geometrical aspects of Toda Fields generalizing the links between Liouville gravity and uniformization of Riemann surfaces of genus greater than one. The framework is the interplay between the hermitian and the holomorphic…
We consider the conformal group of a space of dim n=p+q, with SO(p,q) metric. The quotient of this group by its homogeneous Weyl subgroup gives a principal fiber bundle with 2n-dim base manifold and Weyl fibers. The Cartan generalization to…
A null vector is an algebraic quantity with square equal to zero. I denote the universal algebra generated by taking all sums and products of null vectors over the real or complex numbers by N. The rules of addition and multiplication in N…
Symmetric teleparallel gravity theories, in which the gravitational interaction is attributed to the nonmetricity of a flat, symmetric, but not metric-compatible affine connection, have been a topic of growing interest in recent studies.…
Quantum theory is formulated as a probabilistic theory on a flat Minkowski space-time, while general theory of relativity is formulated on a curved manifold as a geometric theory. Bohmian Quantum Gravity approach indicates that one need to…
Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to…
Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non…
The Lax pair formulation of the two dimensional induced gravity in the light-cone gauge is extended to the more general $w_N$ theories. After presenting the $w_2$ and $w_3$ gravities, we give a general prescription for an arbitrary $w_N$…
The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational…
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We…
General relativity can be formally derived as a flat spacetime theory, but the consistency of the resulting curved metric's light cone with the flat metric's null cone has not been adequately considered. If the two are inconsistent, then…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…