×

Geometric approach to quantum theory. (English) Zbl 1436.81018

Summary: We formulate quantum theory taking as a starting point the cone of states.

MSC:

81P05 General and philosophical questions in quantum theory
46A40 Ordered topological linear spaces, vector lattices
46A20 Duality theory for topological vector spaces
17C90 Applications of Jordan algebras to physics, etc.

Keywords:

state; cone; quantum
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Foot, R. and Joshi, G. C., Space-time symmetries of superstring and {J}ordan algebras, International Journal of Theoretical Physics, 28, 12, 1449-1462, (1989) · Zbl 0711.17017 · doi:10.1007/BF00671588
[2] Hanche-Olsen, Harald and St{\o}rmer, Erling, Jordan operator algebras, Monographs and Studies in Mathematics, 21, viii+183, (1984), Pitman (Advanced Publishing Program), Boston, MA · Zbl 0561.46031
[3] Jordan, Pascual and von Neumann, John and Wigner, Eugene Paul, On an algebraic generalization of the quantum mechanical formalism, The Collected Works of {E}ugene {P}aul {W}igner, {P}art {A, 298-333, (1993), Springer-Verlag, Berlin} · doi:10.1007/978-3-662-02781-3_21
[4] Kac, V. G., Classification of simple {\(Z\)}-graded {L}ie superalgebras and simple {J}ordan superalgebras, Communications in Algebra, 5, 13, 1375-1400, (1977) · Zbl 0367.17007 · doi:10.1080/00927877708822224
[5] Kac, V. G. and Martinez, C. and Zelmanov, E., Graded simple {J}ordan superalgebras of growth one, Memoirs of the American Mathematical Society, 150, 711, x+140 pages, (2001) · Zbl 0997.17020 · doi:10.1090/memo/0711
[6] Schwarz, Albert, Scattering matrix and inclusive scattering matrix in algebraic quantum field theory
[7] Vinberg, E. B., The theory of convex homogeneous cones, Trudy Moskovskogo Matemati\v{c}eskogo Ob\v{s}\v{c}estva, 12, 340-403, (1963) · Zbl 0138.43301
[8] Vinberg, E. B., Structure of the group of automorphisms of a homogeneous convex cone, Trudy Moskovskogo Matemati\v{c}eskogo Ob\v{s}\v{c}estva, 13, 56-83, (1965) · Zbl 0224.17010
[9] Vinberg, E. B. and Gindikin, S. G. and Pyatetskii-Shapiro, I. I., Classification and canonical realization of complex homogeneous bounded domains, Trudy Moskovskogo Matemati\v{c}eskogo Ob\v{s}\v{c}estva, 12, 404-437, (1963) · Zbl 0137.05603
[10] Xu, Yichao, Theory of complex homogeneous bounded domains, Mathematics and its Applications, 569, x+427, (2005), Kluwer Academic Publishers, Dordrecht · Zbl 1115.32014 · doi:10.1007/1-4020-2133-X
[11] Schwarz, A. S. and Tyupkin, Yu. S., Measurement theory and the {S}chr\"{o}dinger equation, Quantum Field Theory and Quantum Statistics, {V}ol. 1, 667-675, (1987), Hilger, Bristol
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.