Uniqueness theorems for classical four-vector fields in Euclidean and Minkowski spaces

Dale A. Woodside

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

Euclidean and Minkowski four-space uniqueness theorems are derived which yield a new perspective of classical four-vector fields The Euclidean four-space uniqueness theorem is based on a Euclidean four-vector identity which is analogous to an identity used in Helmholtz's theorem on the uniqueness of three-vector fields. A Minkowski space identity and uniqueness theorem can be formulated from first principles and the space components of this identity turn out to recuce to the three-vector Helmholtz's identity in a static Newtonian limit. A further result is a uniqueness theorem for scalar fields based on an identity which is proved to be a static Newtonian limit of the zeroth or scalar component of the Minkowski space extension of the Helmholtz identity. Last, the three-vector Helmholtz identity and uniqueness theorem and their four-space extensions to Minkowski space are generalized to mass damped fields.

Original languageEnglish
Pages (from-to)4911-4943
Number of pages33
JournalJournal of Mathematical Physics
Volume40
Issue number10
DOIs
Publication statusPublished - Oct 1999

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