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 SIGMA 16 (2020), 020, 3 pages       arXiv:1906.04939     
https://doi.org/10.3842/SIGMA.2020.020 
Contribution to the Special Issue on Algebra, Topology, and Dynamics in Interaction in honor of Dmitry Fuchs 
Geometric Approach to Quantum Theory
Albert Schwarz
 Department of Mathematics, UC Davis, Davis, CA 95616, USA
 
 
Received February 29, 2020, in final form March 25, 2020; Published online April 01, 2020
 Abstract 
We formulate quantum theory taking as a starting point the cone of states.
 Key words: state; cone; quantum. 
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References 
- Foot R., Joshi G.C., Space-time symmetries of superstring and Jordan algebras, Internat. J. Theoret. Phys. 28 (1989), 1449-1462.
 
- Hanche-Olsen H., Størmer E., Jordan operator algebras, Monographs  and Studies in Mathematics, Vol. 21, Pitman (Advanced Publishing Program),  Boston, MA, 1984.
 
- Jordan P., von Neumann J., Wigner E.P., On an algebraic generalization of the  quantum mechanical formalism, in The Collected Works of Eugene Paul  Wigner, Part A, The Scientific Papers, Vol. I, Springer-Verlag,  Berlin, 1993, 298-333.
 
- Kac V.G., Classification of simple $Z$-graded Lie superalgebras and simple  Jordan superalgebras, Comm. Algebra 5 (1977), 1375-1400.
 
- Kac V.G., Martinez C., Zelmanov E., Graded simple Jordan superalgebras of  growth one, Mem. Amer. Math. Soc. 150 (2001), x+140 pages.
 
- Schwarz A., Scattering matrix and inclusive scattering matrix in algebraic quantum field theory, arXiv:1908.09388.
 
- Schwarz A.S., Tyupkin Yu.S., Measurement theory and the Schrödinger  equation, in Quantum Field Theory and Quantum Statistics, Vol. 1, Hilger,  Bristol, 1987, 667-675.
 
- Vinberg E.B., The theory of convex homogeneous cones, Trans. Moscow  Math. Soc. 12 (1963), 340-403.
 
- Vinberg E.B., Structure of the group of automorphisms of a homogeneous convex  cone, Trans. Moscow Math. Soc. 13 (1965), 56-83.
 
- Vinberg E.B., Gindikin S.G., Pyatetskii-Shapiro I.I., Classification and  canonical realization of complex homogeneous bounded domains, Trans.  Moscow Math. Soc. 12 (1963), 404-437.
 
- Xu Y., Theory of complex homogeneous bounded domains, Mathematics and  its Applications, Vol. 569, Kluwer Academic Publishers, Dordrecht, 2005.
 
 
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