Gauge theory and the Higgs mechanism based on differential geometry in the discrete space [ital M][sub 4][times][ital Z][sub [ital N]]

Journal Article · Fri Jul 15 00:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.50.1026· OSTI ID:7180895

Okumura, Y ^[1]

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1. Department of Natural Sciences, Chubu University, Kasugai, Aichi, 487 (Japan)

Weinberg-Salam theory and SU(5) grand unified theory (GUT) are reconstructed using the generalized differential calculus extended on the discrete space [ital M][sub 4][times][ital Z][sub [ital N]]. Our starting point is the generalized gauge field expressed by [ital A]([ital x],[ital n])= mJ[sub [ital i]] a[sub [ital i]][sup [degree]]([ital x],[ital n])[ital scrda][sub [ital i]]([ital x],[ital n]), (n=1,2,...,[ital N]), where [ital a][sub [ital i]]([ital x],[ital n]) is the square matrix valued function defined on [ital M][sub 4][times][ital Z][sub [ital N]] and [ital scrd]=[ital d]+ mJ[sub [ital m]=1][sup [ital N]][ital d][sub [chi][ital m]] is a generalized exterior derivative. We can construct the consistent algebra of [ital d][sub [chi][ital m]] which is an exterior derivative with respect to [ital Z][sub [ital N]] and the spontaneous breakdown of gauge symmetry is coded in [ital d][sub [chi][ital m]]. The unified picture of the gauge field and Higgs field as the generalized connection in noncommutative geometry is realized. Not only the Yang-Mills-Higgs Lagrangian but also the Dirac Lagrangian, invariant against the gauge transformation, is reproduced through the inner product between the differential forms. Three sheets ([ital Z][sub 3]) are necessary for Weinberg-Salam theory including strong interaction and the SU(5) GUT. Our formalism is applicable to a more realistic model such as the SO(10) unification model.

• OSTI ID: 7180895
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 50:2; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Pa
GRAND UNIFIED THEORY
DIFFERENTIAL GEOMETRY
SU-5 GROUPS
WEINBERG-SALAM GAUGE MODEL
COMMUTATION RELATIONS
GAUGE INVARIANCE
HIGGS BOSONS
SYMMETRY BREAKING
ELEMENTARY PARTICLES
FIELD THEORIES
GEOMETRY
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICS
PARTICLE MODELS
POSTULATED PARTICLES
SU GROUPS
SYMMETRY GROUPS
UNIFIED GAUGE MODELS
UNIFIED-FIELD THEORIES
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