Related papers: Gibbs and Quantum Discrete Spaces
A discrete quantum process is defined as a sequence of local states $\rho_t$, $t=0,1,2,...$, satisfying certain conditions on an $L_2$ Hilbert space $H$. If $\rho =\lim\rho_t$ exists, then $\rho$ is called a global state for the system. In…
Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. Here we develop Stein's method for the class of discrete Gibbs measures with a density $e^V$, where $V$ is the energy…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
An approach to the discrete quantum gravity based on the Regge calculus is discussed which was developed in a number of our papers. Regge calculus is general relativity for the subclass of general Riemannian manifolds called piecewise flat…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
This article summarizes the Quantum Bayesian point of view of quantum mechanics, with special emphasis on the view's outer edges---dubbed QBism. QBism has its roots in personalist Bayesian probability theory, is crucially dependent upon the…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…
Measurement is of central interest in quantum mechanics as it provides the link between the quantum world and the world of everyday experience. One of the features of the latter is its robust, objective character, contrasting the delicate…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
Suggested theory involves a drastic revision of a role of local internal symmetries in physical concept of curved geometry. Under the reflection of fields and their dynamics from Minkowski to Riemannian space a standard gauge principle of…
In a previous work General Relativity has been presented as a microscopic theory of finite and discrete point-like fields that we associate to a classical description of gravitons. The standard macroscopic continuous field is retrieved as…
Quantum theories of gravity are generally expected to have some degree of non-locality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy…
Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are…
At the beginning of the previous century, Newtonian mechanics fell victim to two new revolutionary theories, Quantum Mechanics (QM) and General Relativity (GR). Both theories have transformed our view of physical phenomena, with QM…
The distribution $g_{cl}$ of a Gibbs cluster point process in $X=\mathbb{R}^{d}$ (with i.i.d. random clusters attached to points of a Gibbs configuration with distribution $g$) is studied via the projection of an auxiliary Gibbs measure…
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…
Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…