Related papers: Origin of fermion generations from extended noncom…
The first part is an introductory description of a small cross-section of the literature on algebraic methods in non-perturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of…
Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of three-dimensional physical space. Our approach to…
Endomorphisms algebras can replace the concept of principal fiber bundle. Gauge theories are reformulated within this algebraic framework and further generalized to unify ordinary connections and Higgs fields. A 'noncommutative Maxwell'…
A spontaneously broken SU(2)xU(1) gauge theory with just one "primordial" generation of fermions is formulated in the context of generally covariant theory which contains two measures of integration in the action: the standard…
We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…
This paper is concerned with the study of the geometry of determinant line bundles associated to families of spectral triples parametrized by the moduli space of gauge equivalent classes of Hermitian connections on a Hermitian finite…
The Carroll algebra is constructed as the $c\to0$ limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null…
The main focus of the present work is to study the Feynman's proof of the Maxwell equations using the NC geometry framework. To accomplish this task, we consider two kinds of noncommutativity formulations going along the same lines as…
We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
We examine the behavior of fermions in the presence of a non-singular thick brane having co-dimension 2. It is shown that one can obtain three trapped zero modes which differ from each other by having different values of angular momentum…
A new mechanism is proposed to explain the appearance of the three known fermion generations in a natural way. The underlying idea is based on the discreteness of the spectrum of solutions of the gap equation appearing in models of…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on…
Using the warped extra dimension geometry of the many-brane extension of the Randall-Sundrum solution, we find a natural explanation for the observed quark masses of the three Standard Model (SM) generations. Localizing massless SM matter…
In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…
We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present…
We consider a supersymmetric model that uses partial compositeness to explain the fermion mass hierarchy and predict the sfermion mass spectrum. The Higgs and third-generation matter superfields are elementary, while the first two matter…
In this paper we consider non-anticommutative field theories in $\mathcal{N} =2$ superspace formalism on three-dimensional manifolds with a boundary. We modify the original Lagrangian in such a way that it preserves half the supersymmetry…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…