相关论文: 2T Physics, Scale Invariance and Topological Vecto…

The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…

We consider classical Teichmuller theory and the geodesic flow on the cotangent bundle of the Teichmuller space. We show that the corresponding orbits provide a canonical description of certain (2+1) gravity systems in which a set of…

Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems in which the equality holds in the uncertainty relations for the components of the angular…

Noncommutative geometry is a mathematical framework that expresses the structure of space-time in terms of operator algebras. By using the tools of quantum mechanics to describe the geometry, noncommutative space-times are expected to give…

Curvature and torsion are the two tensors characterizing a general Riemannian spacetime. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the…

A kind of topological field theory is proposed as a candidate to describe the global structure of the 2-form Einstein gravity with or without a cosmological constant. Indeed in the former case, we show that a quantum state in the candidate…

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line…

General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…

Within the twistorial parametrization of Loop Quantum Gravity we investigate the consequences of choosing a spacelike normal vector in the linear simplicity constraints. The amplitudes for the $SU(2)$ boundary states of Loop Quantum…

Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…

On the affine space containing the space $\mathcal{S}$ of quantum states of finite-dimensional systems there are contravariant tensor fields by means of which it is possible to define Hamiltonian and gradient vector fields encoding relevant…

It is well known that the quantum double structure plays an important role in three dimensional quantum gravity coupled to matter field. In this paper, we show how this algebraic structure emerges in the context of three dimensional…

This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…

The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Riemannian metric (tetrad field) is the corresponding Higgs…

In the framework of the two-form gravity, which is classically equivalent to the Einstein gravity, the one-loop effective potential for the conformal factor of metric is calculated in the finite volume and in the finite temperature by…

We present a new quantization scheme for $2D$ gravity coupled to an $SU(2)$ principal chiral field and a dilaton; this model represents a slightly simplified version of stationary axisymmetric quantum gravity. The analysis makes use of the…

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are…

Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is…

We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…

Based on a unified quantum field theory of spinors assumed to describe all matter fields and their interactions we construct the space time structure of general relativity according to a general connection within the corresponding spinor…