Abstract

The power series representing the characteristic function of a regular semisymmetric system involves four linearly independent rotational invariants XA (A = 1, …, 4) that jointly satisfy a quadratic identity. When the XA are appropriately chosen, this takes the form − (X1)2 − (X2)2− (X3)2 + (X4)2 = 0. The XA are thus the components of a null vector in a four-dimensional Euclidean space whose metric is gAB : = diag(− 1, − 1, − 1, 1). Such a vector is equivalent to a simple 2-spinor ξα. The intrinsic presence of a spin vector in the formalism used hitherto suggests that it might be of advantage to replace the latter with an explicit 2-spinor formalism. A way of doing this is examined.

© 1995 Optical Society of America

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