Related papers: Krajewski diagrams and the Standard Model
The Standard Model is the paradigm of particle physics which gives an accurate theory for fundamental particle interactions. However, the extension of Standard Model with higher-order derivatives is not a well-studied subject. This paper is…
The Yang-Mills theory is part of the Standard Model of particle physics. The lack of the mathematical understanding of the theory stands out in theoretical physics. In order to address this problem we observe that a recently proposed…
Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper…
Using the general theory of [10] ( hep-th 9412058 ), quantum Poincar\'e groups (without dilatations) are described and investigated. The description contains a set of numerical parameters which satisfy certain polynomial equations. For most…
We study the combinatorial representation theory of the ``planar rook algebra" $P_n$. This algebra has a basis consisting of planar rook diagrams and multiplication given by diagram concatenation. For each integer $0 \le k \le n$, we…
Perez-Izquierdo and Shestakov recently extended the PBW theorem to Malcev algebras. It follows from their construction that for any Malcev algebra $M$ over a field of characteristic $\ne 2, 3$ there is a representation of the universal…
It is shown that algebra of quantum space of the title of the present paper may be realized on usual unphysical Minkowskii one. Equations of field theory and there solutions are discussed. Solution equations of particle motion are obtained…
We formulate conditions under which the asymptotically expanded spectral action on an almost commutative manifold is renormalizable as a higher-derivative gauge theory. These conditions are of graph theoretical nature, involving the…
Feynman diagrams are a pictorial way of describing integrals predicting possible outcomes of interactions of subatomic particles in the context of quantum field physics. It is highly desirable to have an intrinsic mathematical…
The higher spin properties of the non-abelian bosonization in the classical theory are investigated. Both the symmetry transformation algebra and the classical current algebra for the non-abelian free fermionic model are linear…
The aim of this work is to find a simple mathematical framework for our established description of particle physics. We demonstrate that the particular gauge structure, group representations and charge assignments of the Standard Model…
The representation theory of involutory (or 'maximal compact') subalgebras of infinite-dimensional Kac-Moody algebras is largely terra incognita, especially with regard to fermionic (double-valued) representations. Nevertheless, certain…
First we argue in an informal, qualitative way that it is natural to enlarge space-time to five dimensions to be able to solve the problem of elementary particle masses. Several criteria are developed for the success of this program.…
This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…
We classify simple representations of Khovanov-Lauda-Rouquier algebras in finite type. The classification is in terms of a standard family of representations that is shown to yield the dual PBW basis in the Grothendieck group. Finally, we…
We present the complete structure of the nonlinear $N=2$ super extension of Polyakov-Bershadsky, $W_3^{(2)}$, algebra with the generic central charge, $c$, at the {\it quantum} level. It contains extra two pairs of fermionic currents with…
We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…
Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the Standard Model at low energies, the unified…
By considering the general properties of approximate units in differentiable algebras, we are able to present a unified approach to characterising completeness of spectral metric spaces, existence of connections on modules, and the lifting…
Several related operator-algebraic constructions for quantum field theory models on Minkowski spacetime are reviewed. The common theme of these constructions is that of a Borchers triple, capturing the structure of observables localized in…