Geometrical realization of scalar electrodynamics

1974 ◽  
Vol 9 (2) ◽  
pp. 355-364 ◽  
Author(s):  
Lay-Nam Chang ◽  
Alan Chodos
Keyword(s):  
Geometrical Realization

Geodesic laminations as geometric realizations of Pisot substitutions

2000 ◽  
Vol 20 (4) ◽  
pp. 1253-1266 ◽  
Author(s):  
VÍCTOR F. SIRVENT
Keyword(s):  
Dynamical System ◽  
Geodesic Lamination ◽  
Geodesic Laminations ◽  
Symbolic Dynamical System ◽  
Geometrical Realization

We construct a geodesic lamination on the hyperbolic disk and a dynamical system defined on this lamination. We prove that this dynamical system is a geometrical realization of the symbolic dynamical system that arises from the following Pisot substitution: $1\rightarrow 12, \dotsc, (n-1) \rightarrow 1n, n\rightarrow 1$.

Twelve points in PG (5, 3) with 95040 self-transformations

1958 ◽  
Vol 247 (1250) ◽  
pp. 279-293 ◽  
Keyword(s):  
Projective Space ◽  
Outer Automorphism ◽  
Special Property ◽  
Steiner System ◽  
Finite Projective Space ◽  
Mathieu Group ◽  
Five Dimensions ◽  
Ordinary Space ◽  
High Degree ◽  
Geometrical Realization

The title of this paper could have been ‘Geometry in five dimensions over GF (3)’ (cf. Edge 1954), or ‘The geometry of the second Mathieu group’, or ‘Duads and synthemes’, or ‘Hexastigms’, or simply ‘Some thoughts on the number 6’. The words actually chosen acknowledge the inspiration of the late H. F. Baker, whose last book (Baker 1946) develops the idea of duads and synthemes in a different direction. The special property of the number 6 that makes the present development possible is the existence of an outer automorphism for the symmetric group of this degree. The consequent group of order 1440 is described abstractly in §1, topologically in §2, and geometrically in §§3 to 7. The kernel of the geometrical discussion is in §5, where the chords of a non-ruled quadric in the finite projective space PG (3, 3) are identified with the edges of a graph having an unusually high degree of regularity (Tutte 1958). It is seen in §4 that the ten points which constitute this quadric can be derived very simply from a ‘hexastigm ’ consisting of six points in PG (4, 3) (cf. Coxeter 1958). The connexion with Edge’s work is described in §6. Then §7 shows that the derivation of the quadric from a hexastigm can be carried out in two distinct ways, sug­gesting the use of a second hexastigm in a different 4-space. It is found in §8 that the consequent configuration of twelve points in PG (5, 3) can be divided into two hexastigms in 66 ways. The whole set of 132 hexastigms forms a geometrical realization of the Steiner system s (5, 6, 12), whose group is known to be the quintuply transitive Mathieu group M 12 , of order 95040. Finally, §9 shows how the same 5-dimensional configuration can be regarded (in 396 ways) as a pair of mutually inscribed simplexes, like Möbius’s mutually inscribed tetrahedra in ordinary space of 3 dimensions.

scholarly journals Yukawa hierarchy transfer based on superconformal dynamics and geometrical realization in string models

2003 ◽  
Vol 2003 (02) ◽  
pp. 022-022 ◽  
Author(s):  
Tatsuo Kobayashi ◽  
Hiroaki Nakano ◽  
Tatsuya Noguchi ◽  
Haruhiko Terao
Keyword(s):  
String Models ◽  
Geometrical Realization

Exact geometrical realization of the Cabibbo–Kobayashi–Maskawa matrix: The catamorphy of quark–lepton families

1991 ◽  
Vol 69 (12) ◽  
pp. 1459-1470 ◽  
Author(s):  
D. H. Wilkinson
Keyword(s):  
Cp Violation ◽  
Geometrical Representation ◽  
Geometrical Realization

It is suggested that the number of quark–lepton families is three as the result of a catamorphy; this is illustrated by a geometrical representation that limits the number of families to three, that most naturally generates 15 quark–lepton fields per family, and that exactly realizes the Cabibbo–Kobayashi–Maskawa matrix. The geometrical representation uniquely requires a 1:λ:λ2:λ3 hierarchy for the weak quark–quark linkages and, together with a supplementary Ansatz that derives from the geometrical representation, entrains CP violation in the [Formula: see text]-system and yields mt = 123 ± 65 GeV/c2 from an analysis of Cabibbo–Kobayashi–Maskawa phenomenology.

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