Related papers: Spin foams, Refinement limit and Renormalization
This paper studies the benefits of pressure-robust discretizations in the scope of optimal control of incompressible flows. Gradient forces that may appear in the data can have a negative impact on the accuracy of state and control and can…
While in the fully-connected limit the solution of the spin-glass model is known, with the existence of a complex transition on a critical line in the temperature-external field phase diagram, in finite dimensions we don't know if a…
Anomaly freedom has been one of the most important issues in canonical quantization of gravity. In a physically meaningful (anomaly free) theory, the constraint operators must be first class, and their commutator algebra is expected to…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
We present an approach to quantum gravity based on the general boundary formulation of quantum mechanics, path integral quantization, spin foam models and renormalization.
The spinfoam approach to quantum gravity rests on a "quantization" of BF theory using 2-complexes and group representations. We explain why, in dimension three and higher, this "spinfoam quantization" must be amended to be made consistent…
The simplicial framework of Engle-Pereira-Rovelli-Livine spin-foam models is generalized to match the diffeomorphism invariant framework of loop quantum gravity. The simplicial spin-foams are generalized to arbitrary linear 2-cell…
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the…
Diffusion models are typically trained using pointwise reconstruction objectives that are agnostic to the spectral and multi-scale structure of natural signals. We propose a loss-level spectral regularization framework that augments…
Spin Foam Models are supposed to be discretised path integrals for quantum gravity constructed from the Plebanski-Holst action. The reason for there being several models currently under consideration is that no consensus has been reached…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…
A parametrized spin model was recently introduced and intended for one-dimensional ferromagnets with a deformable Zeeman energy. This model is revisited and given more realistic interpretation in terms of a model for ferromagnetic systems…
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
This paper aims to study the functional renormalization group for quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$. By fixing the gauge symmetry in the construction of the FRG, that breaks the $O(N)$-symmetry and…
This article is aimed at extending the framework of optimal control techniques to the situation where the control field values are restricted to a finite set. We propose a generalization of the standard GRAPE algorithm suited to this…
We suggest a renewed view on non-renormalizable interactions treated perturbatively within a kinematically dependent renormalization procedure. It is based on the usual BPHZ R-operation which is equally applicable to any local QFT…
Dipolar spin ensembles with random spin positions attract much attention currently because they help to understand decoherence as it occurs in solid state quantum bits in contact with spin baths. Also, these ensembles are systems which may…