Related papers: Holonomy Spin Foam Models: Definition and Coarse G…
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…
Employing the world line spinning particle picture we discuss the appearance of several different `gauges' which we use to gain a deeper explanation of the Collective/Gravity identification. We discuss transformations and algebraic…
The U(N) framework and the spinor representation for loop quantum gravity are two new points of view that can help us deal with the most fundamental problems of the theory. Here, we review the detailed construction of the U(N) framework…
In the context of spin foam models for quantum gravity, group field theories are a useful tool allowing on the one hand a non-perturbative formulation of the partition function and on the other hand admitting an interpretation as…
A recently developed viewpoint on the fundamentals of density-functional theory for finite interacting spin-lattice systems that centers around the notion of degeneracy regions is presented. It allows for an entirely geometrical description…
Starting from Ooguri's construction for $BF$ theory in three (and four) dimensions, we show how to construct a well defined theory with an infinite number of degrees of freedom. The spin network states that are kept invariant by the…
We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We…
We propose a spin foam model for pure gauge fields coupled to Riemannian quantum gravity in four dimensions. The model is formulated for the triangulation of a four-manifold which is given merely combinatorially. The Riemannian…
Spin foams of 4d gravity were recently extended from complexes with purely spacelike surfaces to complexes that also contain timelike surfaces. In this article, we express the associated partition function in terms of vertex amplitudes and…
We present a computationally efficient general first-principles based method for spin-lattice simulations for solids. Our method is based on a combination of atomistic spin dynamics and molecular dynamics, expressed through a spin-lattice…
The improved lattice regularization method of the Ashtekar connection holonomy representation in loop quantum gravity is described in this article. The approach is based on the geometric expansion of holonomies into power series up to the…
Lattice gauge theories in varying dimensions, lattice volumes, and truncations offer a rich family of targets for Hamiltonian simulation on quantum devices. In return, formulating quantum simulations can provide new ways of thinking about…
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…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
For each lattice one can define a free boson theory propagating on the corresponding torus. We give an alternative definition where one employs any automorphism of the group $M^*/M$. This gives a wealth of conformal data, which we realize…
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents' degrees of freedom and interaction forces. Starting point is the exact and general coarse…
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
Extending the results of \cite{Heem}, \cite{KLRS} on the holographic representation of local gauge field operators in anti de Sitter space, here we construct the bulk operators for higher spin gauge fields in the leading order of…
Just as 3d state sum models, including 3d quantum gravity, can be built using categories of group representations, "2-categories of 2-group representations" may provide interesting state sum models for 4d quantum topology, if not quantum…
Soft nanocomposites represent both a theoretical and an experimental challenge due to the high number of the microscopic constituents that strongly influence the behaviour of the systems. An effective theoretical description of such systems…