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An Introduction to Space–Time Exterior Calculus

Author

Listed:
  • Ivano Colombaro

    (Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain)

  • Josep Font-Segura

    (Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain)

  • Alfonso Martinez

    (Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain)

Abstract

The basic concepts of exterior calculus for space–time multivectors are presented: Interior and exterior products, interior and exterior derivatives, oriented integrals over hypersurfaces, circulation and flux of multivector fields. Two Stokes theorems relating the exterior and interior derivatives with circulation and flux, respectively, are derived. As an application, it is shown how the exterior-calculus space–time formulation of the electromagnetic Maxwell equations and Lorentz force recovers the standard vector-calculus formulations, in both differential and integral forms.

Suggested Citation

  • Ivano Colombaro & Josep Font-Segura & Alfonso Martinez, 2019. "An Introduction to Space–Time Exterior Calculus," Mathematics, MDPI, vol. 7(6), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:564-:d:242093
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