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International Journal of Theoretical Physics

, Volume 44, Issue 11, pp 2007–2020 | Cite as

Wronski Brackets and the Ferris Wheel

  • Keye Martin
Article
  • 50 Downloads

Abstract

We connect the Bayesian order on classical states to a certain Lie algebra on \(C^\infty[0,1]\). This special Lie algebra structure, made precise by an idea we introduce called a Wronski bracket, suggests new phenomena the Bayesian order naturally models. We then study Wronski brackets on associative algebras, and in the commutative case, discover the beautiful result that they are equivalent to derivations.

Key Words

quantum information Lie algebras domain theory 

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REFERENCES

  1. Abramsky, S. and Jung, A. (1994). Domain theory. In Handbook of Logic in Computer Science, S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, eds., vol. III. Oxford University Press.Google Scholar
  2. Alberti, P. M. and Uhlmann, A. (1982). Stochasticity and Partial Order: Doubly Stochastic Maps and Unitary Mixing, D. Reidel ed. Dordrecht, Boston.Google Scholar
  3. Birkhoff, G. and von Neumann, J. (1936). The logic of quantum mechanics. Annals of Mathematics 37, 823–843.CrossRefMathSciNetGoogle Scholar
  4. Coecke, B. and Martin, K. (2002). A Partial Order on Classical and Quantum States, Oxford University Computing Laboratory, Research Report PRG-RR-02-07, http://web.comlab. ox.ac.uk/oucl/publications/tr/ rr-02-07.htmlGoogle Scholar
  5. Coecke, B. and Martin, K. (2004). Partiality in physics. Invited paper at “Quantum theory: Reconsideration of the foundations 2,” Vaxjo University Press Vaxjo, Sweden. http://arxiv.org/abs/quant-ph/0312044.Google Scholar
  6. L. K. Grover. %Quantum mechanics helps in searching for a needle in a haystack. %Physical Review Letters, 78:325, 1997.CrossRefADSGoogle Scholar
  7. Martin, K. (2003). Entropy as a Fixed Point, Oxford University Computing Laboratory, Research Report PRG-RR-03-05, February 2003, http://web.comlab.ox.ac.uk/oucl/publications/tr/rr-03-05.html.Google Scholar
  8. Martin, K. (2004). Wronski Brackets and the Ferris Wheel, Oxford University Computing Laboratory, Research Report PRG-RR-04-05, April 2004, http://web.comlab.ox.ac.uk/oucl/publications/tr/ rr-04-05.html.Google Scholar
  9. Marshall, A. W. and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications, Academic Press, New York.Google Scholar
  10. Muirhead, R. F. (1903). Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society 21, 144–157. CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Keye Martin
    • 1
  1. 1.Department of MathematicsTulane UniversityNew Orleans

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