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Register a new userEight types of physical arrows distinguished by Newtonian space-time symmetry
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J. Hlinka
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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.
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