Vertex normal ordering as a consequence of nonsymmetric bilinear forms in Clifford algebras

Abstract

We consider Clifford algebras with nonsymmetric bilinear forms. They parametrize the chosen ideal in the isomorphism class of the standard symmetric ones. Since the content of physical theories depends on the injection ⊕nΛn𝒱→CL(𝒱,Q), one has to transform to the standard construction. The injection is described by the antisymmetric part of the bilinear form. This process results in the appropriate vertex normal ordering terms, which are now obtained from the theory itself and not added ad hoc via a regularization argument.