相关论文: A quantum Goldman bracket in 2+1 quantum gravity

Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at the Planck scale is essential for making progress in quantum gravity. The holonomy and Wilson loop of the Levi-Civita connection are…

In this article we propose a new construction of the spatial scalar curvature operator in (1+3)-dimensional LQG based on the twisted geometry. The starting point of the construction is to express the holonomy of the spin connection on a…

Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only…

We develop parallel transport on path spaces from a differential geometric approach, whose integral version connects with the category theoretic approach. In the framework of 2-connections, our approach leads to further development of…

Protocols for observing gravity induced entanglement typically comprise the interaction of two particles prepared either in a superposition of two discrete paths, or in a continuously delocalized (harmonic oscillator) state of motion. An…

A new set of twisted geometric variables is introduced to parametrize the holonomy-flux phase space in loop quantum gravity. It is verified that these new geometric variables, after symplectic reduction with respect to the Gauss constraint,…

Black hole entropy is one of the few windows toward the quantum aspects of gravitation and its study over the years have highlighted the holographic nature of gravity. At the non-perturbative level in quantum gravity, promising explanations…

A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by…

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…

We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this…

By explicit construction, we show that one can in a simple way introduce and measure gravitational holonomies and Wilson loops in lattice formulations of nonperturbative quantum gravity based on (Causal) Dynamical Triangulations. We use…

This paper introduces a (2+1)-dimensional Gaussian field which has the Gaussian free field on the upper half-plane with zero boundary conditions as certain two-dimensional sections. Along these sections, called space-like paths, it matches…

I argue that the first-order formalism recently found to describe classical 2+1-Gravity with matter, is also able to include higher topologies. The present gauge, which is conformal with vanishing York time, is characterized by an analytic…

The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…

We discuss a new approach to computing the standard algebraic operations on homotopy classes of loops in surfaces: the homological intersection number, Goldman's Lie bracket, and the author's Lie cobracket. Our approach uses fillings of the…

After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic…

This is the second paper in the series to introduce a graphical method to loop quantum gravity. We employ the graphical method as a powerful tool to calculate the actions of the Euclidean Hamiltonian constraint operator and the so-called…

We review and systematize recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space-times $\R\times\Sigma^g$, where $\Sigma^g$ is a compact Riemann surface of genus $g$. The emphasis is on quantizations…

We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…

We show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open…