Clifford Algebra Approach to Superenergy Tensors

TL;DR

This paper introduces a Clifford algebra-based method for constructing superenergy tensors from arbitrary tensors, simplifying proofs of their dominant superenergy property across various dimensions.

Contribution

It provides a more compact Clifford algebra formulation for superenergy tensors, enabling easier proofs of their properties in any dimension.

Findings

Clifford algebra approach simplifies superenergy tensor construction

Proof of dominant superenergy property is generalized to all dimensions

New algebraic framework enhances understanding of superenergy tensors

Abstract

Senovilla has recently defined an algebraic construction of a superenergy tensor T{A} from any arbitrary tensor A, by structuring it as an r-fold form. This superenergy tensor satisfies automatically the dominant superenergy property. We present a more compact definition using the r-direct product Clifford algebra r-Cl(p,q). This form for the superenergy tensors allows to obtain an easy proof of the dominant superenergy property valid for any dimension.