Related papers: Diffeomorphisms and spin foam models

In a recent series of papers [1--3], a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data.…

It is shown that the recently observed and unexplained behavior for the spin diffusion in 3He films can be understood in terms of the Fermi liquid theory, provided nonperturbative effects characteristic of the two dimensions are taken into…

We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.

Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…

We investigate the fate of diffeomorphisms when the radial gauge is imposed in canonical general relativity. As shown elsewhere, the radial gauge is closely related to the observer's observables. These observables are invariant under a…

This thesis is devoted to the study of 3-dimensional quantum gravity as a spin foam model and group field theory. In the first part of this thesis, we review some general physical and mathematical aspects of 3-dimensional gravity, focusing…

Various fluid mechanical systems, governed by nonlinear differential equations, enjoy a hidden, higher-dimensional dynamical Poincar\'e symmetry, which arises owing to their descent from a Nambu-Goto action. Also, for the same reason, there…

We show that every effective smooth action of a Lie group G on a manifold M is a diffeomorphism from G onto its image in Diff(M), where the image is equipped with the subset diffeology of the functional diffeology.

This essay summarizes the state of the art on some aspects of the dynamics of polynomial diffeomorphsms in complex dimension two, and it presents a number of open questions.

Analysis with the characteristic functional of stochastic motion is used for the gradient spin echo measurement of restricted motion to clarify details of the diffraction-like effect in a porous structure. It gives the diffusive diffraction…

In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We then used this correspondence to give a geometric proof of the…

Local action principles on a manifold $\M$ are invariant (if at all) only under diffeomorphisms that preserve the boundary of $\M$. Suppose, however, that we wish to study only part of a system described by such a principle; namely, the…

We study the state-sum models of quantum gravity based on a representation 2-category of the Poincare 2-group. We call them spin-cube models, since they are categorical generalizations of spin-foam models. A spin-cube state sum can be…

Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a…

We approach the question of complexification of the diffeomorphism group of the circle by considering real-analytic maps from the circle into the punctured complex plane with winding number +1. Such complex deformations form an…

Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large…

Capturing and predicting the effective mechanical properties of highly porous cellular media still represents a significant challenge for the research community, due to their complex structural interdependencies and known size effects.…

Let the DRO (Diffeomorphism, Reparametrization, Observer) algebra DRO(N) be the extension of $diff(N)\oplus diff(1)$ by its four inequivalent Virasoro-like cocycles. Here $diff(N)$ is the diffeomorphism algebra in $N$-dimensional spacetime…

We consider a description of membranes by (2,1)-dimensional field theory, or alternatively a description of irrotational, isentropic fluid motion by a field theory in any dimension. We show that these Galileo-invariant systems, as well as…

Robotic tasks often require motions with complex geometric structures. We present an approach to learn such motions from a limited number of human demonstrations by exploiting the regularity properties of human motions e.g. stability,…