Related papers: Gauge theory for families
This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…
Six different models, straightforward extensions of the standard model to SU(3)_c X SU(3)_L X U(1)_X, which do not contain particles with exotic electric charges are described. Two of the models are one family and four are three family…
The values of color and anticolor charges are proposed. The structure of gluons is predicted relative to their color and anticolor charges. It is shown that the gauge bosons of lower order theories can be used as it is for higher order…
Families of smooth closed oriented 4-manifolds with a complex spin structure are studied by means of a family version of the Bauer--Furuta invariants in the context of parametrised stable homotopy theory, leading to a definition of…
In this paper we will analyze the quantization of a gauge theory on a four sphere. This will be done by mode expanding all the fields in the theory in terms of harmonic modes. We will also analyse the BRST symmetry of this theory.
We present a Sugawara-type construction for boundary charges in 4d BF theory and in a general family of related TQFTs. Starting from the underlying current Lie algebra of boundary symmetries, this gives rise to well-defined quadratic…
In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which…
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the…
Homeomorphisms allowing us to prove topological equivalences between one-parameter families of maps undergoing the same bifurcation are constructed in this paper. This provides a solution for a classical problem in bifurcation theory that…
When discussing the gauge symmetries of any theory, the Henneaux-Teitelboim transformations are often underappreciated or even completely ignored, due to their on-shell triviality. Nevertheless, these gauge transformations play an important…
We discuss the relation between spacetime diffeomorphisms and gauge transformations in theories of the Yang-Mills type coupled with Einstein's General Relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of…
We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…
In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…
Here is summarized the gauge theoretical formulation and quantization of two popular gravity theories in (1+1)-dimensional time.
Gauge theories are formulated on the noncommutative two-sphere. These theories have only finite number of degrees of freedom, nevertheless they exhibit both the gauge symmetry and the SU(2) "Poincar\'e" symmetry of the sphere. In…
In third quantization the origin of fermion families is easy to understand: the electron field, the muon field and the tau field are identical fields in precisely the same sense as three electrons are identical and undistinguishable…
We bring a linkage from representation theory of Lie groups to homotopy theory for maps between flag manifolds. As applications we derive from representation theory abundant families of homotopy classes of maps between flag manifolds whose…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
We consider a differential geometric setting on power sets and Borel algebras. Our chosen framework is based on diffeologies, and we make a link between the various diffeological structures that we propose, having in mind set-valued maps,…
In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and…