Related papers: Standard model and unimodularity condition
We interpret the unimodularity condition in almost commutative geometries as central extensions of spin lifts. In Connes' formulation of the standard model this interpretation allows to compute the hypercharges of the fermions.
Standard model is minimally extended using the unitary group $G'=U(3)\times SU(2)\times U(1)$ of Connes' color-flavor algebra. In place of Connes' unimodularity condition an extra Higgs is assumed to spontaneously break $G'$ down to…
A short review of recent renormalization group analyses of the self-consistence of the Standard Model is presented.
Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…
It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$…
It is well known that anomaly cancellation {\it almost} determines the hypercharges in the standard model. A related (and somewhat more stronger) phenomenon takes place in Connes' NCG framework: unimodularity (a technical condition on…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
We give a new criterion for solvability of group equations, providing proofs of various generalizations of the Kervaire-Laudenbach conjecture for Connes-embeddable groups.
I define a naturalness criterion formalizing the intuitive notion of naturalness discussed in the literature. After that, using $\phi^4$ as an example, I demonstrate that a theory may be natural in the $MS$-scheme and, at the same time,…
We give a formula for the modular operator and modular conjugation in terms of matrix coefficients of corepresentations of a quantum group in the sense of Kustermans and Vaes. As a consequence, the modular autmorphism group of a unimodular…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an…
We argue that moduli in the adjoint representation of the standard- model gauge group are a natural feature of superstring models, and that they can account for the apparent discrepancy between the string and unification scales.
We present a concise review of the status of the Standard Model and of the search for new physics.
A regularization of the Cross-Newell equation is presented. It is based on a secondary re-modulation along characteristics. This new characteristic Cross-Newell equation is not isotropic (has preferred directions), but is universal…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…
A general procedure is presented which associates to a finite crossed module a premodular category, generalizing the representation categories of a finite group and of its double, and the extent to which the resulting category fails to be…
The successes and shortcomings of the Standard Model are reviewed, with emphasis on the reasons motivating the need to extend it. The basic elements of grand unification and supersymmetry are described, exploring their phenomenological…
In this letter we show a kind of \mt gauge symmetry can be unified into a simple group with the standard model gauge symmetry in the context of coset space unification. We also discuss some implication from one of this kind of unification.