Multivector Functionals

TL;DR

This paper introduces multivector functionals, explores derivative operators like directional derivatives, curl, divergence, and gradient, and rigorously proves derivation rules with detailed examples, expanding the mathematical framework for multivector calculus.

Contribution

It develops the foundational theory of multivector functionals and derivative operators, providing rigorous proofs and detailed examples for the first time.

Findings

Defined multivector functionals and derivative operators

Proved derivation rules rigorously

Provided detailed examples of derivations

Abstract

In this paper we introduce the concept of \emph{multivector functionals.} We study some possible kinds of derivative operators that can act in interesting ways on these objects such as, e.g., the $A$-directional derivative and the generalized concepts of curl, divergence and gradient. The derivation rules are rigorously proved. Since the subject of this paper has not been developed in previous literature, we work out in details several examples of derivation of multivector functionals.