相关论文: Some minor examples on discrete geometry

Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}'…

Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…

We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. These are systems where the kinematics of small perturbations are dominated by an effective…

Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…

We review the main consequences of the possible existence of a minimum measurable length, of the order of the Planck scale, on quantum effects occurring in black hole physics. In particular, we focus on the ensuing minimum mass for black…

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…

It is shown that the theory of dark matter can be derived from the first principles. Particles representing a new form of matter gravitate but do not interact electromagnetically, strongly and weakly with the known elementary particles.…

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…

We argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime. Most importantly, these are derived dynamically…

Recently much work has been done in lowering the Planck threshold of quantum gravitational effects (sub-millimeter dimension(s), Horava-Witten fifth dimension, strings or branes low energy effects, etc.). Working in the framework of 4-dim…

Some physically interesting weak-gravitational effects and phenomena are reviewed and briefly discussed: particle geometric phases due to the time-dependent spin-rotation couplings, non-inertial gravitational wave in rotating reference of…

We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…

Quantum gravitational effects become significant at a cut-off species scale that can be much lower than the Planck scale whenever we get a parametrically large number of fields becoming light. This is expected to occur at any perturbative…

This paper begins with a theoretical explanation of why spacetime is discrete. The derivation shows that there exists an elementary length which is essentially Planck's length. We then show how the existence of this length affects time…

For field theories in curved spacetime, defining how matter gravitates is part of the theory building process. In this letter, we adopt Bekenstein's multiple geometries approach to allow part of the matter sector to follow the geodesics on…

Didactic heuristic arguments, based on the quantum mechanics of the vacuum and the structure of spacetime, are reviewed concerning particle creation from the vacuum by an electric field, vacuum radiation in an accelerated frame, black-hole…

We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the…

The scale of quantum mechanical effects in matter is set by Planck's constant, $\hbar$. This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and…

Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…

It is proposed that gravity may arise in the low energy limit of a model of matter fields defined on a special kind of a dynamical random lattice. Time is discretized into regular intervals, whereas the discretization of space is random and…