Description
An Algebraic Dynamical System (ADS) is a new formalism by which one can describe side by side classical and quantum physical systems. It is completely equivalent with the usual formulation, but has the advantage that it is easier to see the similarities and differences between the two systems. Its first justification is elegance; the possibilities of unifying different theories. There are, however, other possibilities. A variant, an Algebraic Covariance System (ACS), in which there is no unique time development, particularly useful for relativistic theories, is in this book used to give a description of algebraic Wightman quantum field theory. A new suggestion is given to attack the longstanding problem of Wightman theory for the electromagnetic quantum field, the so-called Gupta-Bleuler problem. For an ADS there is a very interesting application, namely to the study of the foundations of quantum theory. This leads to extremely surprising and also provocative results. A future publication will be devoted to this.
