Octonions and unified theories with orthogonal groups

1977 ◽  
Vol 18 (14) ◽  
pp. 441-446 ◽  
Author(s):  
F. Buccella ◽  
M. Falcioni ◽  
A. Pugliese
Keyword(s):  
Orthogonal Groups ◽  
Unified Theories

Water, Water, Here and There

2018 ◽  
Author(s):  
Steven E. Vigdor
Keyword(s):  
Quark Mass ◽  
Mass Difference ◽  
Baryon Number ◽  
Electroweak Phase Transition ◽  
Hydrogen Burning ◽  
Quark Masses ◽  
Grand Unified Theories ◽  
Down Quark ◽  
Unified Theories ◽  
The Stability

Chapter 4 deals with the stability of the proton, hence of hydrogen, and how to reconcile that stability with the baryon number nonconservation (or baryon conservation) needed to establish a matter–antimatter imbalance in the infant universe. Sakharov’s three conditions for establishing a matter–antimatter imbalance are presented. Grand unified theories and experimental searches for proton decay are described. The concept of spontaneous symmetry breaking is introduced in describing the electroweak phase transition in the infant universe. That transition is treated as the potential site for introducing the imbalance between quarks and antiquarks, via either baryogenesis or leptogenesis models. The up–down quark mass difference is presented as essential for providing the stability of hydrogen and of the deuteron, which serves as a crucial stepping stone in stellar hydrogen-burning reactions that generate the energy and elements needed for life. Constraints on quark masses from lattice QCD calculations and violations of chiral symmetry are discussed.

scholarly journals Low-dimensional representations of finite orthogonal groups

2021 ◽  
pp. 1-22
Author(s):  
KAY MAGAARD ◽  
GUNTER MALLE
Keyword(s):  
Orthogonal Groups ◽  
Brauer Characters ◽  
Low Dimensional

Abstract We determine the smallest irreducible Brauer characters for finite quasi-simple orthogonal type groups in non-defining characteristic. Under some restrictions on the characteristic we also prove a gap result showing that the next larger irreducible Brauer characters have a degree roughly the square of those of the smallest non-trivial characters.

scholarly journals STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

2021 ◽  
pp. 1-48
Author(s):  
Federico Scavia
Keyword(s):  
Finite Groups ◽  
Reductive Groups ◽  
Orthogonal Groups ◽  
De Rham Cohomology ◽  
Algebraic Stacks ◽  
Steenrod Operations ◽  
De Rham

Abstract Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

scholarly journals Grand unified theories in renormalisable, classically scale invariant gravity

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Martin B. Einhorn ◽  
D.R. Timothy Jones
Keyword(s):  
Scale Invariant ◽  
Grand Unified Theories ◽  
Unified Theories

scholarly journals Higher pullbacks of modular forms on orthogonal groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Brandon Williams
Keyword(s):  
Modular Forms ◽  
Differential Operators ◽  
Jacobi Form ◽  
Siegel Modular Forms ◽  
Orthogonal Groups

Abstract We apply differential operators to modular forms on orthogonal groups O ⁢ ( 2 , ℓ ) {\mathrm{O}(2,\ell)} to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are preserved; in particular, the higher pullbacks of the lift of a (lattice-index) Jacobi form ϕ are theta lifts of partial development coefficients of ϕ. For certain lattices of signature ( 2 , 2 ) {(2,2)} and ( 2 , 3 ) {(2,3)} , for which there are interpretations as Hilbert–Siegel modular forms, we observe that the higher pullbacks coincide with differential operators introduced by Cohen and Ibukiyama.

scholarly journals Accidental SO(10) axion from gauged flavour

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Luca Di Luzio
Keyword(s):  
Mass Window ◽  
High Quality ◽  
High Scale ◽  
Quality Problem ◽  
Axion Mass ◽  
Grand Unified Theories ◽  
Unified Theories ◽  
Canonical Dimension ◽  
General Perspective ◽  
Effective Operators

Abstract An accidental U(1) Peccei-Quinn (PQ) symmetry automatically arises in a class of SO(10) unified theories upon gauging the SU(3)f flavour group. The PQ symmetry is protected by the ℤ4 × ℤ3 center of SO(10) × SU(3)f up to effective operators of canonical dimension six. However, high-scale contributions to the axion potential posing a PQ quality problem arise only at d = 9. In the pre-inflationary PQ breaking scenario the axion mass window is predicted to be ma ∈ [7 × 10−8, 10−3] eV, where the lower end is bounded by the seesaw scale and the upper end by iso-curvature fluctuations. A high-quality axion, that is immune to the PQ quality problem, is obtained for ma ≳ 2 0.02 eV. We finally offer a general perspective on the PQ quality problem in grand unified theories.

Précis ofUnified theories of cognition

1992 ◽  
Vol 15 (3) ◽  
pp. 425-437 ◽  
Author(s):  
Allen Newell
Keyword(s):  
Cognitive Science ◽  
Full Range ◽  
Cognitive Architecture ◽  
Convincing Evidence ◽  
Syllogistic Reasoning ◽  
Human Cognition ◽  
Unified Theory ◽  
Theoretical Concepts ◽  
Wide Range ◽  
Unified Theories

AbstractThe book presents the case that cognitive science should turn its attention to developing theories of human cognition that cover the full range of human perceptual, cognitive, and action phenomena. Cognitive science has now produced a massive number of high-quality regularities with many microtheories that reveal important mechanisms. The need for integration is pressing and will continue to increase. Equally important, cognitive science now has the theoretical concepts and tools to support serious attempts at unified theories. The argument is made entirely by presenting an exemplar unified theory of cognition both to show what a real unified theory would be like and to provide convincing evidence that such theories are feasible. The exemplar is SOAR, a cognitive architecture, which is realized as a software system. After a detailed discussion of the architecture and its properties, with its relation to the constraints on cognition in the real world and to existing ideas in cognitive science, SOAR is used as theory for a wide range of cognitive phenomena: immediate responses (stimulus-response compatibility and the Sternberg phenomena); discrete motor skills (transcription typing); memory and learning (episodic memory and the acquisition of skill through practice); problem solving (cryptarithmetic puzzles and syllogistic reasoning); language (sentence verification and taking instructions); and development (transitions in the balance beam task). The treatments vary in depth and adequacy, but they clearly reveal a single, highly specific, operational theory that works over the entire range of human cognition, SOAR is presented as an exemplar unified theory, not as the sole candidate. Cognitive science is not ready yet for a single theory – there must be multiple attempts. But cognitive science must begin to work toward such unified theories.

scholarly journals Orthogonal groups containing a given maximal torus

2003 ◽  
Vol 266 (1) ◽  
pp. 87-101 ◽  
Author(s):  
Rosali Brusamarello ◽  
Pascale Chuard-Koulmann ◽  
Jorge Morales
Keyword(s):  
Maximal Torus ◽  
Orthogonal Groups
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