Clifford algebra and the projective model of homogeneous metric spaces: Foundations

This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to physicists and engineers and the emphasis is on explanation rather than rigorous proof. The projective model is based on projective geometry and Clifford algebra. It supplements and enhances vector and matrix algebras. It also subsumes complex numbers and quaternions. Projective geometry augmented with Clifford algebra provides a unified algebraic framework for describing points, lines, planes, etc, and their transformations, such as rotations, reflections, projections, and translations. The model is relevant not only to Euclidean space but to a variety of homogeneous metric spaces.Comment: 89 pages, 140 figures (many include 3D PRC vector graphics

Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs

This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases