131 research outputs found
Superconnections and the Higgs Field
Within the mathematical framework of Quillen, one interprets the Higgs field
as part of the superconnection on a superbundle. We propose to take as
superbundle the exterior algebra obtained from a Hermitian bundle with
structure group U(n). Spontaneous symmetry breaking appears as a consequence of
a non-vanishing scalar curvature. The U(1) Higgs model reformulates the
Ginzburg-Landau theory, while the U(2) model relates to the electroweak theory
with the relation for the gauge coupling constants, the formula
for the Weinberg angle, and the ratio
for the masses (squared) of the W, Z, and Higgs boson (at tree level).Comment: 21 pages, Latex, references added, minor change of conten
A nonperturbative form of the spectral action principle in noncommutative geometry
Using the formalism of superconnections, we show the existence of a bosonic
action functional for the standard K-cycle in noncommutative geometry, giving
rise, through the spectral action principle, only to the Einstein gravity and
Standard Model Yang-Mills-Higgs terms. It provides an effective nonminimal
coupling in the bosonic sector of the Lagrangian.Comment: 12 pages. LaTeX2e, instructions for obsolete LaTeX'
Superconnections: an Interpretation of the Standard Model
The mathematical framework of superbundles suggests that one considers the
Higgs field as a natural constituent of a superconnection. I propose to take as
superbundle the exterior algebra obtained from a Hermitian vector bundle of
rank 5 for the Standard Model.Comment: 10 pages, LaTeX2e, AMS fonts. To appear in Electr.J.Diff. E
Geometrical Interpretation of BRST Symmetry in Topological Yang-Mills-Higgs Theory
We study topological Yang-Mills-Higgs theories in two and three dimensions
and topological Yang-Mills theory in four dimensions in a unified framework of
superconnections. In this framework, we first show that a classical action of
topological Yang-Mills type can provide all three classical actions of these
theories via appropriate projections. Then we obtain the BRST and anti-BRST
transformation rules encompassing these three topological theories from an
extended definition of curvature and a geometrical requirement of Bianchi
identity. This is an extension of Perry and Teo's work in the topological
Yang-Mills case. Finally, comparing this result with our previous treatment in
which we used the ``modified horizontality condition", we provide a meaning of
Bianchi identity from the BRST symmetry viewpoint and thus interpret the BRST
symmetry in a geometrical setting.Comment: 16 pages, LaTeX fil
Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra
In Yang-Mills theory, the charges of the left and right massless Fermions are
independent of each other. We propose a new paradigm where we remove this
freedom and densify the algebraic structure of Yang-Mills theory by integrating
the scalar Higgs field into a new gauge-chiral 1-form which connects Fermions
of opposite chiralities. Using the Bianchi identity, we prove that the
corresponding covariant differential is associative if and only if we gauge a
Lie-Kac super-algebra. In this model, spontaneous symmetry breakdown naturally
occurs along an odd generator of the super-algebra and induces a representation
of the Connes-Lott non commutative differential geometry of the 2-point finite
space.Comment: 17 pages, no figur
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