Related papers: Picture changing operators in supergeometry and su…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
Transformers have significantly advanced the field of natural language processing, but comprehending their internal mechanisms remains a challenge. In this paper, we introduce a novel geometric perspective that elucidates the inner…
The geometry of antisymmetric fields with nontrivial transitions over a base manifold is described in terms of exact sequences of cohomology groups. This formulation leads naturally to the appearance of nontrivial topological charges…
We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…
We introduce new techniques for calculations in Gauge theories with extended supersymmetry. We are working in Projective Superspace where the $SU(2)$ R-symmetry is realized geometrically by including an auxilliary $\mathbb{CP}^1$ component…
We set up some foundations of generalised scheme theory related to new incompressible symmetric tensor categories. This is analogous to the relation between super schemes and the category of super vector spaces.
The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose…
We recall the notion of a differential operator over a smooth map (in linear and non-linear settings) and consider its versions such as formal $\hbar$-differential operators over a map. We study constructions and examples of such operators,…
Continuing our exploration of maximally supersymmetric gauge theories (MSYM) deformed by higher dimensional operators, in this paper we consider an off-shell approach based on pure spinor superspace and focus on constructing supersymmetric…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
It is proposed the generalized action functional for N=1 superparticle in D=3,4,6 and 10 space-time dimensions. The superfield geometric approach equations describing superparticle motion in terms of extrinsic geometry of the worldline…
The geometrical (superembedding) approach is used as a tool for deriving from the worldvolume dynamics of superbranes field theoretical models exhibiting partial supersymmetry breaking. In this way we obtain nonlinear actions for Goldstone…
We briefly review superstring theories, highlighting the important concepts, developments, and open problems of the subject.
The complete classification of the irreducible representations of the N-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields is presented. Off-shell invariant actions of one-dimensional…
Problem of global integration of geometric structures arising in the theory of dynamical systems admitting the normal shift is considered. In the case when such integration is possible the problem of globalization for shift maps is studied.
Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…
Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.