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Quantum Field Theory for Quantum Finance

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Abstract

This chapter introduces a general overview of four major concepts and models in quantum theory: quantum mechanics, quantum field theory, Feynman’s path integral, and quantum anharmonic oscillators. These four concepts with models in quantum theory form critical mass to establish the basic theoretical and mathematical models in quantum finance theory in next chapter, namely, Feynman’s path integral model of quantum finance (also known as first generation of quantum finance) and quantum anharmonic model of quantum finance (also known as second generation of quantum finance). To avoid complex mathematical derivations, this chapter focuses on the basic concepts of quantum theory with its related models that are crucial to understand the mathematical and quantum model in quantum finance.

Anyone who is not shocked by quantum theory has not understood it.

Niels Bohr (1885–1962)

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References

  • Assche, G. (2006) Quantum Cryptography and Secret-Key Distillation. Cambridge University Press; 1 edition.

    Google Scholar 

  • Baaquie, B. (2018) Quantum Field Theory for Economics and Finance. Cambridge University Press. 1st edition.

    Google Scholar 

  • Becherrawy, T. (2012) Electromagnetism: Maxwell Equations, Wave Propagation and Emission. Wiley-ISTE; 1 edition, 2012.

    Google Scholar 

  • Blaise, P. and Henri-Rousseau O. (2011) Quantum Oscillators. Wiley.

    Google Scholar 

  • Bohr, N. (1913) On the Constitution of Atoms and Molecules, Part I” (PDF). Philosophical Magazine. 26 (151): 1–24.

    Google Scholar 

  • Davisson, C. J. and Germer, L. H. (1928) Reflection of Electrons by a Crystal of Nickel. Proceedings of the National Academy of Sciences of the United States of America. 14 (4): 317–322.

    Article  Google Scholar 

  • Einstein, A. (1905) Ăśber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt [On a Heuristic Viewpoint Concerning the Production and Transformation of Light]. Annalen der Physik (Berlin) (in German). Hoboken, NJ (published 10 March 2006). 322 (6): 132–148.

    Article  Google Scholar 

  • Einstein, A., Podolsky, B., Rosen, N. (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review 47 (10): 777–780.

    Article  Google Scholar 

  • Feynman, R. P. (1948) Space-Time Approach to Non-Relativistic Quantum Mechanics. Reviews of Modern Physics. 20 (2): 367–387.

    Article  MathSciNet  Google Scholar 

  • Feynman, R. P.; Hibbs, A. R. (1965) Quantum Mechanics and Path Integrals. New York: McGraw-Hill.

    Google Scholar 

  • Gilyarov V. L. and Slutsker, A. I. (2010) Energy features of a loaded quantum anharmonic oscillator. Physics of the Solid State 52(3): 585–590.

    Article  Google Scholar 

  • Heisenberg, W. (1925) Ăśber quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zeitschrift fĂĽr Physik. 33 (1): 879–893.

    Google Scholar 

  • LaloĂ«, F. (2012) Applications of quantum entanglement. In Do We Really Understand Quantum Mechanics? Cambridge University Press, 150–167.

    Google Scholar 

  • PoorLeno (2019) Hydrogen Density Plots. https://commons.wikimedia.org/w/index.php?title=File:Hydrogen_Density_Plots.png&oldid=343305978. Accessed 21 Aug 2019.

  • Padmanabhan, T. (2016) Quantum Field Theory: The Why, What and How (Graduate Texts in Physics). Springer.

    Google Scholar 

  • Padilla A. and PĂ©rez, J. (2012) A Simulation Study of the Fundamental Vibrational Shifts of HCl Diluted in Ar, Kr, and Xe: Anharmonic Corrections Effects. International Journal of Spectroscopy, 2012: 1–7.

    Article  Google Scholar 

  • Planck, M. (1901) Ueber das Gesetz der Energieverteilung im Normalspectrum [On the law of the distribution of energy in the normal spectrum]. Annalen der Physik. 4 (3): 553–563.

    Article  Google Scholar 

  • Plotnitsky, A. (2010) Epistemology and Probability: Bohr, Heisenberg, Schrödinger, and the Nature of Quantum-Theoretical Thinking (Fundamental Theories of Physics). Springer.

    Google Scholar 

  • Sen, A. (1926) Quantum Entanglement and its Applications. Current Science 112(7): 1361, 2017.

    Article  Google Scholar 

  • Schrödinger, E. An Undulatory Theory of the Mechanics of Atoms and Molecules. Physical Review 28: 1049–1070.

    Article  Google Scholar 

  • Schrödinger, E. (1935) Discussion of probability relations between separated systems. Mathematical Proceedings of the Cambridge Philosophical Society. 31 (4): 555–563.

    Article  Google Scholar 

  • Yanofsky, N. S. and Mannucci, M. A. (2008) Quantum Computing for Computer Scientists. Cambridge University Press; 1 edition.

    Google Scholar 

  • Young, T. (1802) The Bakerian Lecture: On the Theory of Light and Colours. Philosophical Transactions of the Royal Society of London. 92: 12–48.

    Google Scholar 

Download references

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Correspondence to Raymond S. T. Lee .

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Lee, R.S.T. (2020). Quantum Field Theory for Quantum Finance. In: Quantum Finance. Springer, Singapore. https://doi.org/10.1007/978-981-32-9796-8_2

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  • DOI: https://doi.org/10.1007/978-981-32-9796-8_2

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