Canonical Reduction of Tensors and the Physical Properties of Condensed Matter: Application to Optics

A general framework for the description of the physical properties of matter by a canonical reduction procedure of tensors is presented; besides geometrical symmetries, this paper emphasizes the role of intrinsic symmetries which are due either to the indiscernability of some of the physical quantities involved or to thermodynamical arguments. The intrinsic symmetries are expressed through the behaviour of the tensors describing the investigated property under the effect of some index permutation. The scheme of reduction of any tensor into parts that are irreducible not only with respect to rotations and inversion but also with respect to index permutations is shown and examples are given in the area of light-matter interaction.

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