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Stochastic variational quantization and maximum entropy principle

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Abstract

In this note, we discuss the stochastic variational method (SVM) to derive the action principle of Schrödinger equation. In this formalism, the wave function is introduced as one of convenient ways to express the action. This work is a reformulation of Nelson—Yasue’s stochastic quantization scheme and its variational formulation by Yasue, and will furnish possible way to deal with more complicated system such as quantum field theory, suggesting an origin of quantum mechanics.

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References

  1. E. Nelson, “Derivation of the Schrödinger equation from Newtonian mechanics,” Phys. Rev. 150, 1079 (1966)

    Article  ADS  Google Scholar 

  2. E. Nelson, Quantum Fluctuations (Princeton Univ. Press, Prinston, NJ, 1985).

    MATH  Google Scholar 

  3. K. Yasue, “Stochastic calculus of variations,” J. Funct. Anal. 41, 327 (1918).

    Article  MathSciNet  Google Scholar 

  4. T. Koide and T. Kodama, “Navier-Stokes, GrossPitaevskii and generalized diffusion equations using stochastic variational method,” J. Phys., A 45, 255204 (2012).

    Article  MathSciNet  ADS  Google Scholar 

  5. T. Koide and T. Kodama, Stochastic Variational Method as Quantization Scheme I: Field Quantization of Complex Klein-Gordon Equation, ArXiv:1306.6922

  6. T. Koide, T. Kodama, and K. Tsushina, Stochastic Variational Method as a Quantization Scheme II: Quantization of Electromagnetic Fields, ArXiv:1406.6295.

  7. T. Takabayasi, “On the formulation of quantum mechanics associated with classical pictures,” Prog. Theor. Phys. 8, 143 (1952)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. T. C. Wallstrom, “On the derivation of the Schrödinger equation from stochastic mechanics,” Found. Phys. Lett. 2, 113 (1989).

    Article  MathSciNet  Google Scholar 

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Correspondence to T. Kodama.

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Kodama, T., Koide, T. Stochastic variational quantization and maximum entropy principle. Phys. Part. Nuclei 46, 768–771 (2015). https://doi.org/10.1134/S1063779615050135

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