Abstract
In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified.
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References
Aerts, D., Aerts, S., Broekaert, J., Gabora, L.: The Violation of Bell Inequalities in the Macroworld. Foundations of Physics 30, 1387–1414 (2000)
Aerts, D., Czachor, M.: Quantum Aspects of Semantic Analysis and Symbolic Artificial Intelligence. Journal of Physics A-Mathematical and General 37, L123–L132 (2004), http://uk.arxiv.org/abs/quant-ph/0309022
Aerts, D., Gabora, L.: A Theory of Concepts and Their Combinations II: A Hilbert Space Representation. Kybernetes 34, 176–205 (2005)
Baaquie, B.E.: Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge University Press, Cambridge (2004)
Ballentine, L.: Quantum Mechanics: A modern development. World Scientific, Singapore (1998)
Barnsley, M.F.: Superfractals: Patterns of nature. Cambridge University Press, Cambridge (2006)
Bruza, P., Cole, R.: Quantum Logic of Semantic Space: An Exploratory Investigation of Context Effects in Practical Reasoning. In: Artemov, S., Barringer, H., d’Avila Garcez, A.S., Lamb, L.C., Woods, J. (eds.) We Will Show Them: Essays in Honour of Dov Gabbay, vol. 1, pp. 339–361. College Publications, London (2005)
Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.): Proceedings of the second conference on Quantum Interaction, March 26-28. College Publications, London (2008)
Bruza, P.D., Kitto, K., Nelson, D., McEvoy, C.L.: Entangling words and meaning. In: Proceedings of the Second Quantum Interaction Symposium (QI 2008), pp. 118–124. College Publications (2008)
Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.): Quantum Interaction. Association for the Advancement of Artificial Intelligence. AAAI Press, Menlo Park (2007)
Bruza, P.D., Widdows, D., Woods, J.A.: Quantum Logic of Down Below. In: Engesser, K., Gabbay, D., Lehmann, D. (eds.) Handbook of Quantum Logic and Quantum Structures, vol. 2. Elsevier, Amsterdam (2007)
Bruza, P.D., Woods, J.H.: Quantum collapse in semantic space: interpreting natural language argumentation. In: Proceedings of the Second Quantum Interaction Symposium (QI 2008), pp. 141–147. College Publications (2008)
Coplien, J.O., Zhao, L.: Symmetry breaking in software patterns. In: Butler, G., Jarzabek, S. (eds.) GCSE 2000. LNCS, vol. 2177, p. 37. Springer, Heidelberg (2001)
Gabora, L., Rosch, E., Aerts, D.: Toward an ecological theory of concepts. Ecological Psychology 20, 84–116 (2008)
Jones, M.N., Mewhort, D.J.K.: Representing Word Meaning and Order Information in a Composite Holographic Lexicon. Psychological Review 114(1), 1–37 (2007)
Khrennikov, A.: Quantum-like Probabilistic Models outside Physics (2007), arXiv:0702250
Kitto, K.: Modelling and Generating Complex Emergent Behaviour. Ph.D thesis, School of Chemistry Physics and Earth Sciences, The Flinders University of South Australia (2006)
Kitto, K.: Why quantum theory? In: Proceedings of the Second Quantum Interaction Symposium, pp. 11–18. College Publications (2008)
Kronz, F.M., Lupher, T.A.: Unitarily Inequivalent Representations in Algebraic Quantum Theory. International Journal of Theoretical Physics 44(8), 1239–1258 (2005)
McArthur, R.M., Bruza, P.D.: Discovery of tacit knowledge and topical ebbs and flows within the utterances of online community. In: Ohsawa, Y., McBurney, P. (eds.) Chance Discovery - Foundations and Applications. Advances in Information Processing, vol. XVI. Springer, Heidelberg (2003)
Peres, A.: Quantum theory: concepts and methods. Fundamental theories of physics, vol. 57. Kluwer academic publishers, Dordrecht (1993)
Umezawa, H.: Advanced Field Theory: Micro, macro, and thermal physics. American Institute of Physics, New York (1993)
Vitiello, G.: My Double Unveiled. John Benjamins Publishing Company, Amsterdam (2001)
Watson, A.: The mathematics of symmetry. New Scientist 1740 (1990)
Weinberg, S.: The Quantum Theory of Fields, vol. 1. Cambridge University Press, Cambridge (1995)
Widdows, D.: Geometry and Meaning. CSLI Publications, Stanford (2004)
Zhao, L., Coplien, J.: Symmetry in Class and Type Hierarchy. In: Noble, J., Potter, J. (eds.) Proceedings Fortieth International Conference on Technology of Objects, Languages and Systems (TOOLS Pacific 2002), Sydney, Australia, pp. 181–190. Australian Computer Society (2002)
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Kitto, K., Bruza, P., Sitbon, L. (2009). Generalising Unitary Time Evolution. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds) Quantum Interaction. QI 2009. Lecture Notes in Computer Science(), vol 5494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00834-4_4
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DOI: https://doi.org/10.1007/978-3-642-00834-4_4
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