Related papers: Non-Archimedean Geometry and Physics on Adelic Spa…
After a brief review of p-adic numbers, adeles and their functions, we consider real, p-adic and adelic superalgebras, superspaces and superanalyses. A concrete illustration is given by means of the Grassmann algebra generated by two…
We introduce a geometric formalism for studying modular forms of half-integral weight and explore some of its basic properties. Geometric Hecke operators are constructed and some basic spaces of $p$-adic forms are introduced. The $p$-adic…
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
The article is devoted to the investigation of particular classes of quasi-invariant descending at infinity measures on linear spaces over non-Archimedean fields such that measures are with values in non-Archimedean fields also. Their…
This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…
This is a compilation of some well known propositions of Alain Connes concerning the use of noncommutative geometry in mathematical physics.
This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…
In this paper, we offer a brief introduction to the $p$-adic numbers and operations in the metric space defined under the $p$-adic norm. Specifically, we provide a clear description of the derivation of the $p$-adic number via the…
On the space $\mathbb Q_p^n$, where $p\ne 2$ and $p$ does not divide $n$, we construct a p-adic counterpart of spherical coordinates. As applications, a description of homogeneous distributions on $\mathbb Q_p^n$ and a skew product…
We discuss recent developments in $p$-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact $p$-adic manifolds" over new period maps on moduli spaces of abelian…
The ``geometry'', in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG), along with resulting, thereby, potential physical…
The article provides an introduction to infinite-dimensional differential calculus over topological fields and surveys some of its applications, notably in the areas of infinite-dimensional Lie groups and dynamical systems.
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
Different aspects of application of non-Euclidian geometries in architectural compositions are considered. These aspects are illustrated by examples of Armenian (medieval and contemporary) architectural compositions.
This note surveys basic topological properties of nonarchimedean analytic spaces, in the sense of Berkovich, including the recent tameness results of Hrushovski and Loeser. We also discuss interactions between the topology of nonarchimedean…
Discussed is mechanics of objects with internal degrees of freedom in generally non-Euclidean spaces. Geometric peculiarities of the model are investigated detailly. Discussed are also possible mechanical applications, e.g., in dynamics of…
p-Adic and adelic generalization of ordinary quantum cosmology is considered. In [1], we have calculated p-adic wave functions for some minisuperspace cosmological models according to the "no-boundary" Hartle-Hawking proposal. In this…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external…