Chiral Structures Under the Standard of Orthogonal Groups

Abstract

General features of microscopic and macroscopic chiral structures can be discussed under the standard of orthogonal group theory. Configuration space of systems, not physical space, is taken into account. This change of perspective allows to overcome traditional shortcomings related to true and false chirality, statistical realization of mirror images, classification of objects as more or less chiral. From this viewpoint, a chiral object is a physical system whose configurations are described by the O(N) algebra in an abstract N-dimensional space. A quantum mechanical interpretation is straightforward due to the fact that combinations of chiral states give rise to parity states which can be interpreted as energy eigenstates.