Inoue, A. and Maeda, Y. (1985) On Integral Transformations Associated with a Certain Lagrangian—As a Prototype of Quantization. Journal of the Mathematical Society of Japan, 37, 219-244.
https://doi.org/10.2969/jmsj/03720219

has been cited by the following article:

• TITLE: Does There Exist the Applicability Limit of PDE to Describe Physical Phenomena?—A Personal Survey of Quantization, QED, Turbulence

  AUTHORS: Atsushi Inoue

  KEYWORDS: Superspace, Grassmann Variables, Hamilton-Jacobi Equation, Quantization

  JOURNAL NAME: World Journal of Mechanics, Vol.14 No.6, June 30, 2024

  ABSTRACT: What does it mean to study PDE (Partial Differential Equation)? How and what to do “to claim proudly that I’m studying a certain PDE”? Newton mechanic uses mainly ODE (Ordinary Differential Equation) and describes nicely movements of Sun, Moon and Earth etc. Now, so-called quantum phenomenum is described by, say Schrödinger equation, PDE which explains both wave and particle characters after quantization of ODE. The coupled Maxwell-Dirac equation is also “quantized” and QED (Quantum Electro-Dynamics) theory is invented by physicists. Though it is said this QED gives very good coincidence between theoretical1 and experimental observed quantities, but what is the equation corresponding to QED? Or, is it possible to describe QED by “equation” in naive sense?