Simplest Quantum Structures and the Foundation of Interaction

The most elementary conceivable quantum structure, referred to as the protyposis, allows for a new approach to interaction, in general, and the shape of concrete gauge groups, in particular. Here it is essential to realize that the conception of interaction is a manifestation of the dynamical layering structure, that is, a hybrid from the region where quantum theory and classical physics are overlapping. As is well known, the four fundamental interactions in physics can be formulated as local gauge theories. Here the electromagnetic and the weak interactions are associated with force quanta that can appear as real objects in space-time. For the corresponding gauge groups a relationship to the space-time concept of the protyposis can be established. The quanta of the strong interaction, by contrast, cannot exist as free objects. Here and, moreover, in gravitation many mathematical problems are open. A gauge-theoretical formulation needs to be founded in a different way.