Longitudinal and transverse components of a vector field

Abstract

A unified account, from a pedagogical perspective, is given of the longitudinal and transverse projective delta functions proposed by Belinfante and of their relation to the Helmholtz theorem for the decomposition of a three-vector field into its longitudinal and transverse components. It is argued that the results are applicable to fields that are time-dependent as well as fields that are time-independent.

9 pages pdf format. Includes derivation and extension of the Frahm relation and volume integrals of projectors

References in corpus (5)

• Angular momentum of the electromagnetic field: the plane wave paradox resolved
• Angular momentum of light
• Equivalence of two mathematical forms for the bound angular momentum of the electromagnetic field
• Derivation of the paraxial form of the angular momentum of the electromagnetic field from the general form
• Regularization of the second-order partial derivatives of the Coulomb potential of a point charge

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