A geometrical approach to the degree of chirality and asymmetry

A new measure of the degree of chirality and asymmetry of a finite number of particles is proposed. To this end a space of configurations of identical particles is defined as the orbit space of the group of all permutations of particles embedded in an Euclidean space. This space is shown to be a metric space and the action of the translation and orthogonal groups is also defined. The results are applied to the study of an algebra of polynomials on the configuration space and its equivalence to the algebra of symmetric Cartesian tensors is demonstrated. An illustrative example is presented. Some general features of chirality are also briefly discussed.