Formalism of Quantum Theory

Olivier Brunet

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of model theory in our study. In particular, we show that our formal theory is complete, meaning that it entirely determines the behaviour of quantum systems. Moreover, we provide a characterization of the models of our formal theory, thus providing new insights in the study of hidden variable models of quantum theory.

Alexander Wilce

Y. B. Band, Y. Avishai

Roderick I. Sutherland

A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a picture of an external reality. The new formalism, developed first for the single-particle case, has the advantage of generalizing immediately to quantum field theory and to the description of relativistic phenomena such as particle creation and annihilation.

François David

Ioan Zaharie, Viorel Laurentiu Cartas

In this paper we apply the path integral formalism for the quantum rigid rotator in 2+1 space time dimension related to the knot theory. The knots theory put the knots into an one to one relation with the braids considered in the braid group theory where braids are actually path into the path integrals formalism. The present work aims the connection between such theories and the anyons behavior.