Related papers: Discrete space-time geometry and skeleton concepti…
We feel that non-commutative geometry is to particle physics what Riemannian geometry is to gravity. We try to explain this feeling.
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
The motion of a particle is studied in a random space-time. It is assumed that the velocity is small enough for the non-relativistic approximation to be valid. The randomness of the metric induces a diffusion in coordinate space. Hence it…
The tubular geometry (T-geometry) is a generalization of the proper Euclidean geometry, founded on the property of sigma-immanence. The proper Euclidean geometry can be described completely in terms of the world function $\sigma =\rho…
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum…
Given a minimum measurable length underlying spacetime, the latter may be effectively regarded as discrete, at scales of order the Planck length. A systematic discretization of continuum physics may be effected most efficiently through the…
This work presents an alternative approach to obtain the quantum field equations in curved spacetime, considering that sufficiently small particles follow stochastic trajectories around geodesic. Our proposal is based on a stochastic…
We show that the dimension of spacetime becomes complex-valued when its short-scale geometry is invariant under a discrete scaling symmetry. This characteristic can generically arise in quantum gravities, for instance, in those based on…
The classical spacetime is usually described by a differentiable manifold with infinitely many degrees of freedom. Occasionally though, it is useful to consider an approximation whose number of degrees of freedom is finite. There are…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…
The third modification of the space-time geometry is considered. (The first modification is the spacial relativity, the second one is the general relativity.) After the third modification of the space-time geometry the motion of free…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…
The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
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…
Development of the contemporary theory of physical phenomena in the microcosm is considered to be a result of development of Einstein's ideas on a possibility of the event space modification and on a possibility of stochastic (Brownian)…
Classical geometry can be described either in terms of a metric tensor $g_{ab}(x)$ or in terms of the geodesic distance $\sigma^2(x,x')$. Recent work, however, has shown that the geodesic distance is better suited to describe the quantum…