Warianty tytułu
Języki publikacji
Abstrakty
The issue of using the physical method in economics is no longer an innovative idea. However, nowadays the methods of mathematical quantum mechanics are also applied to economic sciences. This is the natural result of the fact that as applicable in quantum mechanics, mathematical spaces and tools turn out to be useful in other fields of science. Then it is possible to assume that the problem of the choice of the space is a universal question that is associated not only with mathematics and physics but also with economics or social sciences. In this paper the author considers various formulations of Hilbert space in relation to finite-dimensional quantum mechanics which constitutes a fundament to also apply my outcomes in economics. On the basis of mathematical considerations the author puts forward the hypothesis that the complex Hilbert space is characterized with numerous advantages in relation to its real and quaternionic alternatives.(original abstract)
Twórcy
- University of Wrocław, Poland
Bibliografia
- Adler S.L. (1995). Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press.
- Adler S.L. (2017). Peres experiment using photons: No test for hypercomplex (quaternionic) quantum theories. Phys. Rev. A 95, 060101 (R).
- Drabik E. (2011). Classical and quantum physics in selected economic models. Fundations of Management. Vol. 3. No. 1.
- Eichberger J., Pirner H.J. (2017). Decision theory with a hilbert space as possibility space. Discussion Paper Series. No. 637. University of Heidelberg, Department of Economics.
- Elsberg D. (1961). Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics. Vol. 75, pp. 643-669.
- Fałda B., Zając J. (2012). Zagadnienie regresji w naukach ekonomicznych. Metody ilościowe w badaniach ekonomicznych. Vol XIII/1, pp. 82-95.
- Kahneman D., Tversky A. (1979). Prospect theory: An analysis of decision under risk. Econometrica. Vol. 47, pp. 263-291.
- Moretti V., Oppio M. (2016). Quantum Theory in Real Hilbert Space, arXiv [math-ph].
- Reed M., Simon B. (1972). Methods of modern mathematical physics. Vol. I. Academic Press. New York. London.
- Savage L.J. (1954). Foundations of Statistics. Wiley. New York.
- Schlichtinger A.M. (2017). O algebrach obserwabli w teorii kwantowej. Praca licencjacka. Uniwersytet Wrocławski.
- Stanimir A. (2005). Analiza korespondencji jako narzędzie do badania zjawisk ekonomicznych. Wydawnictwo Akademii Ekonomicznej. Wrocław.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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