Related papers: Operator Spin Foams: holonomy formulation and coar…
We formulate the spin foam representation of discrete SU(2) gauge theory as a product of vertex amplitudes each of which is the spin network generating function of the boundary graph dual to the vertex. In doing so the sums over spins have…
The observation of strongly-correlated states in moir\'e systems has renewed the conceptual interest in magnetic systems with higher SU(4) spin symmetry, e.g. to describe Mott insulators where the local moments are coupled spin-valley…
Loop quantum gravity has provided us with a canonical framework especially devised for background independent and diffeomorphism invariant gauge field theories. In this quantization the fundamental excitations are called spin network…
We survey and analyze different ways in which bornologies, coarse structures and uniformities on a group agree with the group operations.
We present the natural arguments for the rationality of a recently proposed simple approach for renormalization which is based solving differential equations. The renormalization group equation is also derived in a natural way and…
In this work we study a Spin Foam model for 4d Riemannian gravity, and propose a new way of imposing the simplicity constraints that uses the recently developed holomorphic representation. Using the power of the holomorphic integration…
We discuss a formalism for the spin correlations and polarizations in two-particle systems with spins half-half, half-one and one-one, and provide the connections between the polarizations and correlations with the joint angular…
We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk…
Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting…
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents $\eta$ and $\delta$, as well as ratios of…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
Operator cutoff regularization based on the original Schwinger's proper-time formalism is examined. By constructing a regulating smearing function for the proper-time integration, we show how this regularization scheme simulates the usual…
The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field…
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…
Recently a block spin renormalization group approach was proposed for the dynamical triangulation formulation of two-dimensional quantum gravity. We use this approach to examine non-perturbatively a particular class of higher derivative…
We explore differential and algebraic operations on the exterior product of spinor representations and their twists that give rise to cohomology, the spin cohomology. A linear differential operator $d$ is introduced which is associated to a…
We give a general definition of spin foam models, and then of models of 4d quantum gravity based on constraining BF theory. We highlight the construction and quantization ambiguities entering model building, among which the choice of…
We have limited our interaction scope to those involving particle-s spin. We then develop operators for handling a many-body treatment of the spin interactions. The results presented show how to promote the particles of the system into the…
After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose…