Related papers: Topos Methods in the Foundations of Physics
Although osmosis is a familiar phenomenon, and of pivotal importance in natural systems, it is seldom explained how it might work on the molecular level (if treated at all in physics text books). The standard treatment of osmosis in…
We discuss how triposes may be understood as generalizations of localic geometric morphisms.
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
This paper is a review of the theory of abelian anyons in planar systems at an introductory level and with focus on the formalism of quantum field theory, but with the aim of clarify the connections between the mathematical structure and…
A condensed survey of various aspects of LEP 1 physics is presented with a critical examination of the ingredients that are available for theoretical predictions. A prototype of comparisons for 2f calculations can be found in…
This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.
A definition of a {\it Realistic} Physics Theory is proposed based on the idea that, at all time, the set of physical properties possessed (at that time) by a system should unequivocally determine the probabilities of outcomes of all…
We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…
We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (resp. connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
We present the set of axioms for topological space with the operation of boundary as primitive notion.
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
This text aims to give a pedagogical introduction into the main concepts of the theory of structure formation in the universe. The text is suited for graduate students of astronomy with a moderate background in general relativity. A special…
What is the role of topos theory in the topos models for quantum theory as used by Isham, Butterfield, Doring, Heunen, Landsman, Spitters and others? In other words, what is the interplay between physical motivation for the models and the…
A simple, non-technical introduction to the pre-big bang scenario is given, emphasizing physical motivations, considerations, and consequences over formalism.
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…
Topos theory has been suggested first by Isham and Butterfield, and then by Isham and Doering, as an alternative mathematical structure within which to formulate physical theories. In particular, it has been used to reformulate standard…
This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.
Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of heigher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hibert-style Axiomatic Method. The new notion of Axiomatic…
The following notes are intended to provide a brief primer in plasma physics, introducing common definitions, basic properties and processes typically found in plasmas. These concepts are inherent in contemporary plasma-based accelerator…