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

TL;DR

This paper introduces a canonical tensor reduction framework that incorporates geometrical and intrinsic symmetries, enhancing the understanding of physical properties in condensed matter and their applications in optics.

Contribution

It develops a comprehensive tensor reduction scheme considering both geometrical and intrinsic symmetries, with applications to light-matter interactions in condensed matter.

Findings

Tensor reduction scheme includes intrinsic symmetries due to indiscernability and thermodynamics.

The framework applies to tensors describing optical properties of matter.

Examples demonstrate the scheme's effectiveness in light-matter interaction analysis.

Abstract

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.