Dirac bilinears in condensed matter physics: Relativistic correction for observables and conjugate electromagnetic fields
Phys. Rev. B 113, 115113 – Published 9 March, 2026
DOI: https://doi.org/10.1103/1zfs-f3s8
Abstract
Inspired by recent developments in electron chirality, we reconsider some microscopic physical quantities that have been overlooked or have received little attention in condensed-matter physics, based on the nonrelativistic limit of the Dirac bilinears in relativistic quantum theory. We identify the expression of physical quantities defined by the four-component Dirac field in terms of the two-component Schrödinger field, which is usually used in condensed-matter physics, and clarify its conjugate electromagnetic field. This consideration bridges the fields of condensed-matter physics, quantum chemistry, and particle physics, and paves the way to electromagnetic control of matter. Our findings provide a means of ab initio quantification of material characters such as chirality and axiality that are unique to low-symmetry materials, and stimulate the systematic search for useful, new functionalities.
