Axioms for Non-Relativistic Quantum Mechanics

Wawrzyniec Guz

Luis Grave de Peralta, Maricela Fernández Lozada, Hira Farooq +3 more

Paul Busch, PEKKA J. LAHTI, Juha-Pekka Pellonpää +1 more

J. LaChapelle

The algebraic approach to quantum mechanics has been vital to the development of quantum theory since its inception, and it has evolved into a mathematically rigorous $C^\ast$-algebraic formulation of the theory's axioms. Conversely, the functional approach in the form of Feynman path integrals is far from mathematically rigorous: Nevertheless, path integrals provide an equally valid and useful formulation of the axioms of quantum mechanics. The two approaches can be merged by employing a notion of functional integration based on topological groups that allows to construct functional integral representations of $C^\ast$-algebras. The merger achieves a hybrid formulation of the axioms of quantum mechanics in which topological groups play a leading role. To illustrate the formalism, we apply the framework to non-relativistic and relativistic quantum mechanics via the Heisenberg and Poincaré groups.

Andreas Schlatter

On the basis of the classical axioms of non relativistic quantum mechanics, we develop a model for the interplay between energy and entropy in the process of quantum measurement and shed light on the scope of some of the axioms with regard to the measurement problem.

Wawrzyniec Guz