SU(3) representation for the polarisation of light
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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.
KeywordsPhotons polarisation density matrix, Stokes parameters SU(3) representation bounds
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