A scalar product for computing fundamental quantities in matter

Abstract

We introduce a systematic way to obtain expressions for computing the amount of fundamental quantities such as helicity and angular momentum contained in static matter, given its charge and magnetization densities. The method is based on a scalar product that we put forward, which is invariant under the ten-parameter conformal group in three-dimensional Euclidean space. Such group is obtained as the static restriction (frequency $\omega =0$) of the symmetry group of Maxwell equations: The fifteen-parameter conformal group in 3+1 Minkowski spacetime. In an exemplary application, we compute the helicity and angular momentum squared stored in a magnetic Hopfion.

References in corpus (7)

• Creation and confirmation of Hopfions in magnetic multilayer systems
• Noncollinear Magnetism in Density Functional Calculations
• Total helicity of electromagnetic fields and matter
• Hopfion Dynamics in Chiral Magnets
• Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy
• Stationary Precession Topological Solitons with Nonzero Hopf Invariant in a Uniaxial Ferromagnet
• A conformally invariant derivation of average electromagnetic helicity

Cited by in corpus (3)

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• A scalar product for the radiation of resonant modes