Covariant Derivative of Fermions and All That

A Generalized Covariant Derivative and U ( 3 )

A generalization of the Yang-Mills covariant derivative, that uses both vector and scalar fields and transforms as a 4-vector contracted with Dirac matrices, is used to simplify the Glashow-Weinberg-Salam model. Since SU (3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U (3) to obtain all the correct quantum numbers. A surplus gauge scalar...

Dark Chocolate and Metabolic Syndrome; Do Polyphenols All that Matter?

Jordan Szabó Algebraic Covariant Derivative Curvature Tensors

We show that if R is a Jordan Szabó algebraic covariant derivative curvature tensor on a vector space of signature (p, q), where q ≡ 1 mod 2 and p < q or q ≡ 2 mod 4 and p < q − 1, then R = 0. This algebraic result yields an elementary proof of the geometrical fact that any pointwise totally isotropic pseudo-Riemannian manifold with such a signature (p, q) is locally symmetric.

Manifestly Gauge Covariant Formulation of Lattice Chiral Fermions

We propose a new formulation of chiral fermions on a lattice, on the basis of a lattice extension of the covariant regularization scheme in continuum field theory. The species doublers do not emerge. The real part of the effective action is just one half of that of Dirac-Wilson fermion and is always gauge invariant even with a finite lattice spacing. The gauge invariance of the imaginary part, ...

Manifestly Gauge Covariant Treatment of Lattice Chiral Fermions II

We propose a new formulation of chiral fermions on a lattice, on the basis of a lattice extension of the covariant regularization scheme in continuum field theory. The species doublers do not emerge. The real part of the effective action is just one half of that of Dirac-Wilson fermion and is always gauge invariant even with a finite lattice spacing. The gauge invariance of the imaginary part, ...