A new mathematical representation for discussing the state of polarisation of an arbitrary beam of partially polarised light is described which makes use of the generators of the group SU(3). This representation is sufficiently general to describe not only physical photons which are transverse but also virtual photons. The correspondence between our representation and the conventional Stokes parameter representation is established and this leads to an equivalent geometrical description of partially polarised light in terms of diametrically opposite points on a Poincarè sphere with radius equal to the degree of polarisation. The connection with the spherical tensor representation is also discussed and this leads to a simple geometrical interpretation of the bounds on the parameters characterizing an arbitrary beam of partially polarised light.

The spin-spin interaction of two arbitrary spin systems is considered in some detail. The temporal evolution of the polarization parameters and the correlation parameters has been worked out. Applications of the formalism and the interpretation of the results to processes such as heavy-ion interactions, muon and nuclear repolarization and depolarization in muonic atoms and interactions of multilevel systems are outlined.

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular groupSU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real linear vector space, are developed in anSU(3) covariant manner. Thef andd symbols ofSU(3) lead to two ways of ‘multiplying’ two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization ofSU(3) is developed as a generalization of that forSU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.