相关论文: Multi-dimensional Virasoro algebra and quantum gra…

A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…

We study field equations for a weak anisotropic model on the tangent Lorentz bundle $TM$ of a spacetime manifold. A geometrical extension of General Relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct…

We construct a mathematical version of quantum field theory. It assigns to a multidimensional variational principle an associative algebra which is a quantization of the Poisson algebra of classical field theory observables. For free scalar…

The non-relativistic versions of the generalized Poincar\'{e} algebras and generalized $AdS$-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by…

It is commonly accepted that the study of 2+1 dimensional quantum gravity could teach us something about the 3+1 dimensional case. The non-perturbative methods developed in this case share, as basic ingredient, a reformulation of gravity as…

In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…

We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian then there exists a…

3-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axi-symmetry. The solution is used to probe several quantum gravity issues. In particular, it is shown that the quantum…

We propose that the Virasoro algebra controls quantum cohomologies of general Fano manifolds $M$ ($c_1(M)>0$) and determines their partition functions at all genera. We construct Virasoro operators in the case of complex projective spaces…

Using the differential calculus on discrete group, we study the general relativity in the space-time which is the product of a four dimensional manifold by a two-point space. We generalize the usual concept of frame and connection in our…

We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…

We analyze the cosmology of a general Scalar-Tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galileon gravity and also the general k-essence type models.…

In this paper, we investigate the generalized Saez-Ballester scalar-tensor theory of gravity via Noether gauge symmetry (NGS) in the background of Bianchi type I cosmological spacetime. We start with the Lagrangian of our model and…

We propose an unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo-Riemannian manifolds enabled with…

Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a…

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…

A model for 2D Quantum Gravity is constructed out of the Virasoro group. To this end the quantization of the abstract Virasoro group is revisited. For the critical values of the conformal anomaly c, some quantum operators (SL(2,R)…

We make a number of remarks on linearized gravity with cosmological constant in any dimension, which, we argue, can be useful in a quantum gravity framework. For this purpose we assume that the background space-time metric corresponds to…

We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the…

In the paper there are investigated various approximate representations of the infinite dimensional $\Bbb Z$--graded Lie algebras: the Witt algebra of all Laurent polynomial vector fields on a circle and its one-dimensional nontrivial…