Related papers: Geometric Aspects of the `Deformation Method'
We study the geometry of the cuspidal edge $M$ in $\mathbb R^3$ derived from its contact with planes and lines (referred to as flat geometry). The contact of $M$ with planes is measured by the singularities of the height functions on $M$.…
The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
A systematic approach is developed in order to obtain spherically symmetric midisuperspace models that accept holonomy modifications in the presence of matter fields with local degrees of freedom. In particular, starting from the most…
At the present work we consider an application of the deformation procedure that enable us to construct, systematically, scalar field models supporting multikinks. We introduce a new deformation function in order to realize this task. We…
Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal $\star$-product and the Wigner functional are obtained by extending the formalism…
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…
We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky-DeWitt (VDW) effective action. We…
We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on…
We introduce a new problem of retrieving 3D models that are deformable to a given query shape and present a novel deep deformation-aware embedding to solve this retrieval task. 3D model retrieval is a fundamental operation for recovering a…
We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting extending the metric formulation of linearized…
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an…
Monocular 3D shape recovery is fundamental to geometric understanding, yet achieving robust generalization across arbitrary viewpoints and unseen object categories remains a significant challenge. In this paper, we present a generalizable…
Reasoning over the interplay between object deformation and force transmission through contact is central to the manipulation of compliant objects. In this paper, we propose Neural Deforming Contact Field (NDCF), a representation that…
Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…
In this paper, we present our study on the $T\bar{T}$-deformation of non-relativistic complex scalar field theory. We find the closed form of the deformed Lagrangian by using the perturbation and the method of characteristics. Furthermore…
In this paper we present a novel approach for representing and evolving deformable active contours. The method combines piecewise regular B{\'e}zier models and curve evolution defined by local Free Form Deformation. The contour deformation…
Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…
This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…