Related papers: The Standard Model within Non-associative Geometry
Scaling and architectural advances have produced strikingly photorealistic image generative models, yet their mechanisms still remain opaque. Rather than advancing scaling, our goal is to strip away complicated engineering tricks and…
We construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) $q$-derivatives. Both theories can be formulated in two different frames, called fractional…
We construct the nonlinear $W(sl(N+3),sl(3))$ algebras and find the spectrum of values of the central charge that gives rise, by contracting the $W(sl(N+3),sl(3))$ algebras, to a $W_3$ algebra belonging to the coset…
We write down three kinds of scale transformations {\tt i-iii)} on the noncommutative plane. {\tt i)} is the analogue of standard dilations on the plane, {\tt ii)} is a re-scaling of the noncommutative parameter $\theta$, and {\tt iii)} is…
We show that in 3-3-1 models there exist a natural relation among the $SU(3)_L$ coupling constant $g$, the electroweak mixing angle $\theta_W$, the mass of the $W$, and one of the vacuum expectation values, which implies that those models…
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…
We describe the construction of theta summable and finitely summable spectral triples associated to Mumford curves and some classes of higher dimensional buildings. The finitely summable case is constructed by considering the stabilization…
We calculate the gauge couplings in the dual standard model. These values are consistent with an associated GeV mass scale, and predict the weak mixing angle to be ${\sin^2 \theta_w} (M_Z) \sim 0.22$.
This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a…
We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a…
In the past year several constructions of non-invertible symmetries in Quantum Field Theory in $d\geq 3$ have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
We discuss how to systematically compute the asymptotic symmetry algebras of generic three-dimensional bosonic higher-spin gauge theories in backgrounds that are asymptotically AdS. We apply these techniques to a one-parameter family of…
Spatial noncommutativity is similar and can even be related to the non-Abelian nature of multiple D-branes. But they have so far seemed independent of each other. Reflecting this decoupling, the algebra of matrix valued fields on…
We compute the nonvanishing spectral torsion functional of the internal part of the noncommutative geometry behind the Standard Model. We show that with a suitable modification of the usual differential graded calculus it matches an…
In this paper we summarize the minimal supersymmetric standard model as well as the renormalization group equations of its parameters. We proceed to examine the feasability of the model when the breaking of supersymmetry is parametrized by…
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
We consider extensions of the Standard Model with neutral scalars in multiplets of $SU(2)$ larger than doublets. When those scalars acquire vacuum expectation values, the resulting masses of the gauge bosons $W^\pm$ and $Z^0$ are not…