Related papers: Higher ideles and class field theory
We investigate the presence of twinlike models in theories described by several real scalar fields. We focus on the first-order formalism, and we show how to build distinct scalar field theories that support the same extended solution, with…
Author's generalization of one-dimensional class field theory to theory of abelian totally ramified p-extensions of a complete discrete valuation field with arbitrary non-separably p-closed residue field and its applications are described.
This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time.…
I summarize and discuss some recent results on formulating actions of six-dimensional superconformal field theories using the language of higher gauge theory. The latter guarantees mathematical consistency of our constructions and we review…
Higher dimensional generalisations of self-duality conditions and of theta angle terms are analysed in Yang-Mills theories. For the theory on a torus, the torus metric and various antisymmetric tensors are viewed as coupling constants…
Effective field theories exploit a separation of scales in physical systems in order to perform systematically improvable, model-independent calculations. They are ideally suited to describe universal aspects of a wide range of physical…
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
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.
We give a function field specific, algebraic proof of the main results of class field theory for abelian extensions of degree coprime to the characteristic. By adapting some methods known for number fields and combining them in a new way,…
If a scalar field theory in (1+1) dimensions possesses soliton solutions obeying first order BPS equations, then, in general, it is possible to find an infinite number of related field theories with BPS solitons which obey closely related…
This is a presentation of explicit methods to construct higher local class field theory by using topological K-groups, explicit symbols and a generalization of Neukirch-Hazewinkel's axiomatic approaches. The existence theorem is discussed…
Hypergroups are lifted to power semigroups with negation, yielding a method of transferring results from semigroup theory. This applies to analogous structures such as hypergroups, hyperfields, and hypermodules, and permits us to transfer…
In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.
We give a classification theorem of certain geometric objects, called torsors over the sheaf of K-theory spaces, in terms of Tate vector bundles. This allows us to present a very natural and simple, alternative approach to the Tate central…
The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.
We construct spaces of 1-dimensional supersymmetric Euclidean field theories and show that they represent real or complex K-theory. A noteworthy feature of our bordism category is that the identity bordism of a point is connected to…
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$…
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially…
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…