scholarly journals Flavor structure from misalignment of inner products in noncommutative geometry

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Masaki J. S. Yang
Keyword(s):  
Noncommutative Geometry ◽  
Inner Products ◽  
Flavor Structure

Dualism QM and GR

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Noncommutative Geometry ◽  
Quantum Tunneling ◽  
Closed Surface ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Surface Integral ◽  
Definition Of

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.

scholarly journals Missing the point in noncommutative geometry

Synthese ◽  
2021 ◽  
Author(s):  
Nick Huggett ◽  
Fedele Lizzi ◽  
Tushar Menon
Keyword(s):  
Scalar Field ◽  
Noncommutative Geometry ◽  
Smooth Manifold ◽  
Operational Definition ◽  
Spectral Triple ◽  
Fundamental Quantity

AbstractNoncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes’ spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar field Moyal–Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry.

scholarly journals Wormhole Solutions in Symmetric Teleparallel Gravity with Noncommutative Geometry

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1260
Author(s):  
Zinnat Hassan ◽  
Ghulam Mustafa ◽  
Pradyumn Kumar Sahoo
Keyword(s):  
Linear Model ◽  
Noncommutative Geometry ◽  
Teleparallel Gravity ◽  
Exponential Model ◽  
Model Parameter ◽  
Exponential Models ◽  
Feasible Solutions ◽  
The Stability ◽  
Tov Equation

This article describes the study of wormhole solutions in f(Q) gravity with noncommutative geometry. Here, we considered two different f(Q) models—a linear model f(Q)=αQ and an exponential model f(Q)=Q−α1−e−Q, where Q is the non-metricity and α is the model parameter. In addition, we discussed the existence of wormhole solutions with the help of the Gaussian and Lorentzian distributions of these linear and exponential models. We investigated the feasible solutions and graphically analyzed the different properties of these models by taking appropriate values for the parameter. Moreover, we used the Tolman–Oppenheimer–Volkov (TOV) equation to check the stability of the wormhole solutions that we obtained. Hence, we found that the wormhole solutions obtained with our models are physically capable and stable.

scholarly journals When are maps preserving semi-inner products linear?

2021 ◽  
Author(s):  
Paweł Wójcik
Keyword(s):  
Hilbert Space ◽  
Infinite Dimensions ◽  
Normed Spaces ◽  
Linear Isometry ◽  
Inner Products ◽  
Finite Dimensional ◽  
Uniformly Smooth ◽  
Non Linear ◽  
Extra Assumption ◽  
Continuous Injection

AbstractWe observe that every map between finite-dimensional normed spaces of the same dimension that respects fixed semi-inner products must be automatically a linear isometry. Moreover, we construct a uniformly smooth renorming of the Hilbert space $$\ell _2$$ ℓ 2 and a continuous injection acting thereon that respects the semi-inner products, yet it is non-linear. This demonstrates that there is no immediate extension of the former result to infinite dimensions, even under an extra assumption of uniform smoothness.

scholarly journals SUSY breaking constraints on modular flavor S3 invariant SU(5) GUT model

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Xiaokang Du ◽  
Fei Wang
Keyword(s):  
Susy Breaking ◽  
Flavor Symmetry ◽  
Modular Invariance ◽  
Lepton Flavor ◽  
Flavor Structure ◽  
Flavor Mixing ◽  
Breaking Mechanism ◽  
Gut Scale ◽  
Additional Constraints ◽  
Rule Out

Abstract Modular flavor symmetry can be used to explain the quark and lepton flavor structures. The SUSY partners of quarks and leptons, which share the same superpotential with the quarks and leptons, will also be constrained by the modular flavor structure and show a different flavor(mixing) pattern at the GUT scale. So, in realistic modular flavor models with SUSY completion, constraints from the collider and DM constraints can also be used to constrain the possible values of the modulus parameter. In the first part of this work, we discuss the possibility that the S3 modular symmetry can be preserved by the fixed points of T2/ZN orbifold, especially from T2/Z2. To illustrate the additional constraints from collider etc on modular flavor symmetry models, we take the simplest UV SUSY-completion S3 modular invariance SU(5) GUT model as an example with generalized gravity mediation SUSY breaking mechanism. We find that such constraints can indeed be useful to rule out a large portion of the modulus parameters. Our numerical results show that the UV-completed model can account for both the SM (plus neutrino) flavor structure and the collider, DM constraints. Such discussions can also be applied straightforwardly to other modular flavor symmetry models, such as A4 or S4 models.

scholarly journals The minimum supersymmetric standard model on noncommutative geometry

2015 ◽  
Vol 2015 (1) ◽  
pp. 13B01-0 ◽  
Author(s):  
M. Shimojo ◽  
S. Ishihara ◽  
H. Kataoka ◽  
A. Matsukawa ◽  
H. Sato
Keyword(s):  
Standard Model ◽  
Supersymmetric Standard Model ◽  
Noncommutative Geometry ◽  
Minimum Supersymmetric Standard Model

Support Vector Machines V: Exploiting Inner Products

NIR news ◽  
2005 ◽  
Vol 16 (3) ◽  
pp. 4-6 ◽  
Author(s):  
Tom Fearn ◽  
Donald J. Dahm
Keyword(s):  
Support Vector Machines ◽  
Support Vector ◽  
Inner Products ◽  
Vector Machines
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