Moment Ideals of Local Dirac Mixtures

Ideals in STA and Dirac fermions

In this paper I reconsider the questions of how the even-grade subalgebra of spacetime algebra can describe fermionic excitations. I start out by analyzing the content of the Pauli-ideals, i.e. the left-lorentz invariant subspaces of the even-grade subalgebra. When interpreted as rotors the general elements in that space describe massless particles with electromagnetic dipolemoments. To study t...

Local Cohomology at Monomial Ideals

Left-ideals, Dirac Fermions and Su (2)-flavour

In this paper I reconsider the use of the left ideals of the even-grade subalgebra of spacetime algebra to describe fermionic excita-tions. When interpreted as rotors the general elements of an even-grade left-ideal describe massless particles in chiral flavour doublets. To study the application of these ideas to the standard Dirac formalism I construct a 2 × 2-matrix representation with bivect...

Local properties of accessible injective operator ideals

In addition to Pisier’s counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a ”good behaviour” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessib...

Toric ideals, real toric varieties, and the moment map

This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties and the moment map. In particular, we explain the relation between linear precision and the moment map.