Related papers: Topos Methods in the Foundations of Physics
The physical models of a successful unified theory about the Universe must operate in different phase of matter evolution and different fields of physics. The attempts to build such wide range theory as a bunch of theories developed for…
In this short note, a topos - called the topos of the connectivity space - is associated with every such space.
Some discussion of physical and geometrical interpretation of Einsteins theory of gravitation which is on basic of cosmology.
In the preprint we present an outline of the one dimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvabilty by radicals, by elementary…
This textbook introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…
We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…
In this paper, we extend the formal definition of topological surgery by introducing new notions in order to model natural phenomena exhibiting it. On the one hand, the common features of the presented natural processes are captured by our…
An axiomatic approach to the mathematical models of the isotropic cosmology.
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…
Topological insulators are a new class of materials that have engendered considerable research interest among the condensed matter community owing primarily to their application prospects in quantum computations and spintronics. Many of the…
This paper introduces the Quantum Contextual Topos (QCT), a novel framework that extends traditional quantum logic by embedding contextual elements within a topos-theoretic structure. This framework seeks to provide a classically-obedient…
This review presents an introduction to Quantum Cosmology, including the mathematical methods essential to the canonical approach, some of the existing conceptual problems and the connection of the models to possible observables.
Logical and mathematical aspects of the basic concepts of thermodynamics are considered.
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by…