SYMMETRY OF INTERACTING VECTOR QUANTITIES

Yu.M. Smirnov and R.M. Grechishkin

Tver State University, Zheliabova Str., 33, 170000 Tver, Russia

The Magnus effect is known to be brought about by the interaction of two quantities: stream velocity v (polar vector) and cylinder rotation velocity in the stream (axial vector). As a result force F springs up (polar vector). The interactions are subject to vector product miltiplication rules pa=P or vF.

Consider now the Hall effect from the same point of view. The electric current in a conductor, with a density j (polar vector), upon interaction with the magnetic field (axial vector) produces an electric field E (polar vector). The F and E quantities may be compared to v and j, respectively, assuming E increasing and j associated with the electron motion. Then it follows that and should correspond to each other. Consequently some kind of rotation should be assumed in analogy to the clockwise rotation of . From the viewpoint of crystal physics the above interactions may be expressed as

,

with infinite symmetry axes being mutually perpendicular.

An existence of four groups of interaction may be supposed when the infinite axes are either mutually perpendicular or when two axes are coinciding. The corresponding examples are known well enough.