Formal Series of Generalised Functions and Their Application to Deformation Quantisation

Abstract

Foundations of the formal series $\ast$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity in formal series calculus is proposed. Problems with defining quantum states over the set of formal series are analysed.

arXiv comment23 pages, some explanation has been added