Geometric and algebraic approaches to quantum theory
- URL: http://arxiv.org/abs/2102.09176v4
- Date: Fri, 15 Oct 2021 06:03:52 GMT
- Title: Geometric and algebraic approaches to quantum theory
- Authors: Albert Schwarz
- Abstract summary: We show how to formulate physical theory taking as a starting point the set of states.
The equations of motion and the formulas for probabilities of physical quantities are analyzed.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We show how to formulate physical theory taking as a starting point the set
of states (geometric approach). We discuss the relation of this formulation to
the conventional approach to classical and quantum mechanics and the theory of
complex systems. The equations of motion and the formulas for probabilities of
physical quantities are analyzed. A heuristic proof of decoherence in our
setting is used to justify the formulas for probabilities. We show that any
physical theory theory can be obtained from classical theory if we restrict the
set of observables. This remark can be used to construct models with any
prescribed group of symmetries; one can hope that this construction leads to
new interesting models that cannot be build in the conventional framework.
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.
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