Related papers: Operator Spin Foams: holonomy formulation and coar…
A number of approaches to four-dimensional quantum gravity, such as loop quantum gravity and holography, situate areas as their fundamental variables. However, this choice of kinematics can easily lead to gravitational dynamics peaked on…
"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams} we introduce. Our diagrams are the spin network analogy of the Feynman diagrams.…
Simple models have played an important role in the discussion of foundational issues in statistical mechanics. Among them the spin--echo system is of particular interest since it can be realized experimentally. This has led to inferences…
Spinons are among the generic excitations in one-dimensional spin systems, they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show…
While the use of spin networks has greatly improved our understanding of the kinematical aspects of quantum gravity, the dynamical aspects remain obscure. To address this problem, we define the concept of a `spin foam' going from one spin…
Multiscale phenomena which include several processes occuring simultaneously at different length scales and exchanging energy with each other, are widespread in magnetism. These phenomena often govern the magnetization reversal dynamics,…
Numerical methods in spin-foam models have significantly advanced in the last few years, yet challenges remain in efficiently extracting results for amplitudes with many quantum degrees of freedom. In this paper we sketch a proposal for a…
In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the…
To study materials phenomena simultaneously at various length scales, descriptions in which matter can be coarse grained to arbitrary levels, are necessary. Attempts to do this in the static regime (i.e. zero temperature) have already been…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
Accurate modeling of spin-orbit coupling and noncollinear magnetism requires noncollinear density functionals within the two-component generalized Kohn-Sham (GKS) framework, yet constructing and implementing noncollinear functionals remains…
We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As part of this formalism we define a modified variation operator which absorbs frame and spin dyad gauge…
Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some "mobility" field. The identity of…
Understanding the large-scale physics is crucial for the spin foam approach to quantum gravity. We tackle this challenge from a statistical physics perspective using simplified, yet feature-rich models. In particular, this allows us to…
In this article we lay foundations for a formal relationship of spin foam models of gravity and BF theory to their continuum canonical formulations. First the derivation of the spin foam model of the BF theory from the discrete BF theory…
The central object of this paper is a holonomy formulation for spin foams. Within this new represen- tation, we analyze three general requirements: locality, composition law, cylindrical consistency. In particular, cylindrical consistency…
We study the issue of coupling among 4-simplices in the context of spin foam models obtained from a group field theory formalism. We construct a generalisation of the Barrett-Crane model in which an additional coupling between the normals…
The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are…
Spin foam models are an attempt for a covariant, or path integral formulation of canonical loop quantum gravity. The construction of such models usually rely on the Plebanski formulation of general relativity as a constrained BF theory and…
This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. For a flat 2--connection, we define the 2-holonomy of…