Related papers: Not too little intervals for quantum mechanics
We explore a new type of discretizations of lattice dynamical models of the Klein-Gordon type relevant to the existence and long-term mobility of nonlinear waves. The discretization is based on non-holonomic constraints and is shown to…
The work aims effective and low-dimensional systems. Some different contexts involving gravitational and electromagnetic interactions are investigated. The electromagnetic one approaches bosonic and fermionic Effective Quantum Field…
This monograph aims to build some new mathematical structures originated from Dyson--Schwinger equations for the description of non-perturbative aspects of gauge field theories whenever bare or running coupling constants are strong enough.
We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra $G$, generalizing the previous construction of discrete…
Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of 3-dimensional quantum gravity involving 6j-symbols are then described, and progress in…
We outline an approach that streamlines considerably the construction and analysis of well-behaved nonlinear quantum dynamics, with completely positive extensions to entangled systems. A few notes are added on the issue of quantum…
We study the cosmological dynamics of non-minimally coupled matter models using the Brown's variational approach to relativistic fluids in General Relativity. After decomposing the Ricci scalar into a bulk and a boundary term, we construct…
Nonequilibrium quantum field theory is often used to derive an approximation for the evolution of number densities and asymmetries in astroparticle models when a more precise treatment of quantum thermal effects is required. This work…
The aim of this monograph is twofold: to explain various nonautonomous integrable systems (discrete Painlev\'e all the way up to the elliptic level, as well as generalizations \`a la Garnier) using an interpretation of difference and…
A search for a problem free cosmology within the framework of an effective non - minimally coupled scalar tensor theory is suggested. With appropriate choice of couplings in variants of a Lee - Wick model [as also in a model supporting Q -…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
We give a leisurely, albeit woefully incomplete, overview of quantum field theory, its relevance to condensed matter systems, and spin systems, which proceeds via a series of illustrative examples. The goal is to provide readers from the…
I argue that the prediction of physical discreteness at the Planck scale in loop gravity is a reasonable conclusion that derives from a sensible ensemble of hypotheses, in spite of some contrary arguments considered in an interesting recent…
We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…
We review a recent proposal for the construction of a quantum theory of the gravitational field. The proposal is based on approximating the continuum theory by a discrete theory that has several attractive properties, among them, the fact…
Many modern theories which try to unify gravity with the Standard Model of particle physics, as e.g. string theory, propose two key modifications to the commonly known physical theories: i) the existence of additional space dimensions; ii)…
Considering bilayer systems as extensions of the planar ones by an internal space of two discrete points, we use the ideas of Noncommutative Geometry to construct the gauge theories for these systems. After integrating over the discrete…
The central idea of this work is the concept of prespace, a hypothetical structure that is postulated to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the implications…
We discuss the classical limit for the long-distance (``soft'') modes of a quantum field when the hard modes of the field are in thermal equilibrium. We address the question of the correct semiclassical dynamics when a momentum cut-off is…
Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad…