Paper detail

Eight types of physical "arrows" distinguished by Newtonian space-time symmetry

The paper draws the attention to the spatiotemporal symmetry of various vector-like physical quantities. The symmetry is specified by their invariance under the action of symmetry operations of the Opechowski nonrelativistic space-time rotation group O(3).{1, 1'}= O'(3), where 1' is time-reversal operation. It is argued that along with the canonical polar vector, there are another 7 symmetrically distinct classes of stationary physical quantities, which can be - and often are - denoted as standard three-components vectors, even though they do not transform as a static polar vector under all operations of O'(3). The octet of symmetrically distinct "directional quantities" can be exemplified by: two kinds of polar vectors (electric dipole moment P and magnetic toroidal moment T, two kinds of axial vectors (magnetization M and electric toroidal moment G), two kinds of chiral "bi-directors" C and F (associated with the so-called true and false chirality, resp.) and still another two achiral "bi-directors" N and L, transforming as the nematic liquid crystal order parameter and as the antiferromagnetic order parameter of the hematite crystal alpha-Fe2O3, respectively.