Vertex Normalordering as a Consequence of Nonsymmetric Bilinearforms in Clifford Algebras

TL;DR

This paper explores how nonsymmetric bilinear forms in Clifford algebras influence vertex normal ordering, providing a natural derivation of these terms from the algebraic structure rather than ad hoc methods.

Contribution

It demonstrates that vertex normal ordering terms can be derived directly from Clifford algebras with nonsymmetric bilinear forms, linking algebraic structure to physical regularization.

Findings

Normal ordering terms arise from the algebraic structure itself.

Transformation to standard symmetric Clifford algebras is essential.

The approach eliminates the need for ad hoc regularization.

Abstract

We consider Clifford algebras with nonsymmetric bilinear forms, which are isomorphic to the standard symmetric ones, but not equal. Observing, that the content of physical theories is dependent on the injection $\oplus^n\bigwedge \V^{(n)}\to CL({\cal V},Q)$ one has to transform to the standard construction. The injection is of course dependent on the antisymmetric part of the bilinear form. This process results in the appropriate vertex normalordering terms, which are now obtained from the theory itself and not added ad hoc via a regularization argument.