Related papers: Higher Topos Theory in Physics
The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant…
Topological Structures in the Standard Model at high $T$ are discussed.
Recent critiques of the semantic conception of scientific theories suggest that a theory is not best formulated as a collection of models satisfying some set of kinematical or dynamical conditions. Thus it has been argued that additional…
We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.
We review some aspects of theories with compact extra dimensions. We consider the motivation and the theoretical basis of Large, Universal and Warped Extra Dimensions. We focus on those aspects that are potentially relevant in the…
Invited contribution to the inaugural issue of {\em Physics Educator.}
We describe some open questions related to support points in the class $S^0$ and introduce some useful techniques toward a higher dimensional Bieberbach conjecture.
We review the prospects for studies of the top quark at the LHC.
Cosmology from the Top Down.
According to the Butterfield--Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However, this paper demonstrates that the current elaborations of this programme neglect quantum…
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…
The earlier history of two--photon physics is reviewed.
This is a reference volume on polyfold and Fredholm theory.
We acuminate the idea of a final theory of physics in order to analyze its logical implications and consequences. It is argued that the rationale of a final theory is the principle of sufficient reason. This implies that a final theory of…
The topos approach to the formulation of physical theories includes a new form of quantum logic. We present this topos quantum logic, including some new results, and compare it to standard quantum logic, all with an eye to conceptual…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
This paper reviews work, largely due to W. Simon and the author, on multipole theory of static spacetimes. The main purpose is to make this work, which lies at the interface of potential theory, conformal geometry and general relativity,…
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.