Geometric and algebraic approaches to quantum theory

Albert Schwarz

Published 2021-02-18Version 1

We show how to formulate quantum theory taking as a starting point the set of states (geometric approach). We give the equations of motion and the formulas for probabilities of physical quantities in this approach. A heuristic proof of decoherence in our setting is used to justify the formulas for probabilities. The geometric approach can be used to formulate quantum theory in terms of Jordan algebras, generalizing the algebraic approach to quantum theory. The scattering theory can be formulated in geometric approach.