Related papers: Diffeomorphisms and spin foam models
Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…
We study spin dynamics of a normal Fermi liquid taking into account the demagnetizing field produced by the spin system itself. Linear solutions of the spin dynamics equations in the form of standing spin waves in a finite volume of liquid…
It is a general belief that the only possible way to consistently deform the Pauli-Fierz action, changing also the gauge algebra, is general relativity. Here we show that a different type of deformation exists in three dimensions if one…
If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains…
We construct covariant theories incorporating fluctuating boundaries and soft cutoffs by introducing dynamical reference frames (DRFs). This framework generalizes the covariant action from a hard-cutoff to a soft-cutoff formulation,…
We classify the possible images of the action of the group of automorphisms of a smooth Fano threefold on its Picard group. We also study the first group cohomology of the Picard group for families of smooth Fano threefolds.
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
We present a controlled mode of "topological" displacement of homogeneous piezo films that arises solely from an inhomogeneous in-plane strain due to an inhomogeneous polarization. For the rotationally symmetric case, we develop a…
We prove large-data local stability theorems for several spin models in two dimensions.
Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, $\xi \colon P \to \Sigma$ a principal $G$-bundle, let $N(\xi)$ denote the moduli space of central Yang-Mills connections on $\xi$, for suitably chosen…
We propose a new systematic approach that allows one to derive the spin foam (state sum) model of a theory starting from the corresponding classical action functional. It can be applied to any theory whose action can be written as that of…
Noise is source of ambiguity for fuzzy systems. Although being an important aspect, the effects of noise in fuzzy modeling have been little investigated. This paper presents a set of tests using three well-known fuzzy modeling algorithms.…
We study the relation between the space of representation classes of the fundamental group of a Riemann surface and gauge theory on trivalent graphs. We construct a partial gauge fixing in the latter gauge theory. As an application we get a…
We first consider M-theory formulated on an open eleven-dimensional spin-manifold. There is then a potential anomaly under gauge transformations on the E_8 bundle that is defined over the boundary and also under diffeomorphisms of the…
The ability of soft matter such as drops and bubbles to change shape dynamically during interaction can give rise to counter-intuitive behaviour that may be expected of rigid materials. Here we show that dimple formation on approach and the…
Through making use of a Borel measure and a piecewise-Riemannian inner scalar product, it is shown that over a Lorentzian manifold every three diffeomorphisms generate a conformal space, whose elements are smooth vector-valued functions…
The diffusion approximation to the relaxation on the distorted Fermi surface in a Fermi liquid is considered. The dependence of the relaxation time on the multipolarity of a Fermi surface deformation is established. The time evolution of…
Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, and $\xi \colon P \to \Sigma$ a principal $G$-bundle. In earlier work we have shown that the moduli space $N(\xi)$ of central Yang- Mills connections, for…
We show how the fixed-spin asymptotics of the EPRL model can be used to perform the spin-sum for spin foam amplitudes defined on fixed two-complexes without interior faces and contracted with coherent spin-network states peaked on a…
Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here,…