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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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