Related papers: On the relation between standard and $\mu$-symmetr…
This paper has several goals. The first idea is to study the geometric PDEs of connection-flatness, curvature-flatness, Ricci-flatness, scalar curvature-flatness in a modern and rigorous way. Although the idea is not new, our main Theorems…
This survey discusses our results and conjectures concerning supersymmetric field theories and their relationship to cohomology theories. A careful definition of supersymmetric Euclidean field theories is given, refining Segal's axioms for…
Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each…
Symmetries of variational problems are considered as symmetries of vector bundle valued exterior differential systems. This approach is then applied to third order ordinary variational equations of motion of the semi-classical spinning…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
We explore extensions of domain theoretic concepts, replacing transitive relations with general non-symmetric distances. These lead to a generalization of Smyth completeness which we characterize in various ways analogous to our previous…
Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string…
We associate to certain symmetric or antisymmetric functions on the set ${E\choose d+1}$ of $(d+1)-$subsets in a finite set $E$ an equivalence relation on $E$ and study some of its properties.
Symmetries are defined in histories-based theories paying special attention to the class of history theories admitting quasitemporal structure (a generalization of the concept of `temporal sequences' of `events' using partial semigroups)…
We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly $|1|$--graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of…
In this paper we describe the geometry of distributions by their symmetries, and present a simplified proof of the Frobenius theorem and some related corollaries. Then, we study the geometry of solutions of $F-$Gordon equation; A PDE which…
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…
Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general c\`adl\`ag semimartingales taking values in Lie groups are defined and investigated. In order to enlarge the class of possible symmetries…
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization…
When we consider a differential equation $\Delta=0$ whose set of solutions is ${{\cal S}}_\Delta$, a Lie-point exact symmetry of this is a Lie-point invertible transformation $T$ such that $T({{\cal S}}_\Delta)={{\cal S}}_\Delta$, i.e. such…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
The generic supersymmetric standard model is a model built from a supersymmetrized standard model field spectrum the gauge symmetries only. The popular minimal supersymmetric standard model differs from the generic version in having…