Abstract
Our knowledge and ignorance concerning the geometry of quantum states are discussed.
Mathematics Subject Classification (2010). Primary 81P16; Secondary 52A20.
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References
G. Birkhoff and J. von Neumann, Ann. of Math. 37, 823–843 (1936).
J. von Neumann,Mathematical Foundations of Quantum Mechanics, PrincetonUniv. Press (1955).
D. Finkelstein, Trans. N.Y. Acad. Sci. 25, 621–637 (1962).
V.S. Varadarajan, Geometry of Quantum Theory, Van Nostrand, vol 1 (1968), vol 2 (1970).
C. Piron, Helv. Phys. Acta, 37, 439–468 (1964); Found. Phys. 2, 287–314 (1972).
B. Mielnik, Commun. Math. Phys. 15, 1–45 (1969).
I. Bengtsson and K. Życzkowski. Geometry of Quantum States, An Introduction to Quantum Entanglement, Cambridge Univ. Press (2006).
B. Mielnik, Commun. Math. Phys. 37, 221–225 (1974).
I. Beng stson, S. Weis and K. Życzkowski, Geometry of the set of mixed quantum states: Apophatic approach, in this volume and preprint arXiv:1112.2347.
A.M. Gleason, J. Math. Mech. 6, 885–893 (1957).
I.M. Gel’fand and M.A. Naimark, Math. Sbornik 12, 197–213 (1943).
R. Haagan d D. Kastler, J. Math. Phys. 5, 848–861 (1964).
J.C.T. Pool, Commun. Math. Phys. 9, 118 (1968); 9, 212 (1968).
H. Araki, Pacific J. Math 50, 309–354 (1979).
R. Haag, Local Quantum Physics, Fields, Particles, Algebras, Springer-Verlag, 2nd Edition (1996).
G.W. Mackey, The mathematical foundations of quantum mechanics, Benjamin, New York (1963).
H. Primas, Chemistry, Quantum Mechanics and Reductionism, Perspectives in Theoretical Chemistry, Springer-Verlag, Berlin-Heidelberg (1983).
G. Ludwig , Z. Phys. 181, 233–260 (1964).
E.B. Davies and J.T. Lewis, Commun. Math. Phys. 17, 239–260 (1970).
R. Penrose, Gen. Rel. Grav. 7, 171–176 (1976).
The Large, the Small and the Human Mind, Cambridge Univ. Press (1997).
T.W.B. Kibble and S. Randjbar-Daemi, J. Phys. A 13, 141–148 (1980).
H. Putnam, The Logic of Quantum Mechanics, Philosophical Papers, vol. 1, Cambridge Univ. Press (1975).
J. Bell and B. Hallet, Philosophy of Science 49, 355–379 (1982).
I. Białlynicki-Birula and J. Mycielski, Annals of Physics 100, 62 (1976).
R. Haagan d U. Bannier, Commun. Math. Phys. 60, 1–6 (1978).
B. Mielnik, Commun. Math. Phys. 101, 323–339 (1985).
N. Gisin, Phys. Lett. A 143,1–2 (1989).
C. Simon, V. Buzek and N. Gisin, Phys. Rev. Lett. 87, 17 (2001).
D.J. Fernandez and B. Mielnik, J. Math. Phys. 35, 2083 (1994).
F. Delgado and B. Mielnik, Phys. Lett. A 249, 369 (1998).
B. Mielnik and O. Rosas-Ortiz, J. Phys. A 37, 10007–10035 (2004).
B. Mielnik and A. Ramirez, Phys. Sci. 84, 045008 (2011).
D.C. Brody, A.C.T. Gustavsson and L.P. Hugston, J. Phys. A 43 082003 (2010).
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Mielnik, B. (2013). Convex Geometry: A Travel to the Limits of Our Knowledge. In: Kielanowski, P., Ali, S., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0448-6_20
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DOI: https://doi.org/10.1007/978-3-0348-0448-6_20
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