Stochastic Variational Method and Quantization

In this talk, we discuss the stochastic variational method (SVM) to derive the action principle of Schrödinger Equation. In this formalism, the wavefunction is not the essential object for Quantum Mechanics but one of convenient ways to express the action. We show that the Canonical Quantization scheme is considered to be a linear representation in complex variables of the consequences of this approach. This work is a kind of reformulation of Nelson’s stochastic quantization scheme and its variational formulation by Yasue. However, we believe that the present form of presentation will furnish possible way to deal with more complicated system such as Quantum Field theory, and also may suggest a new direction to discuss the origin of the Quantum Mechanics, for example, as a consequence of stochastic hidden noises for our space-time conceptIn this talk, we discuss the stochastic variational method (SVM) to derive the action principle of Schrödinger Equation. In this formalism, the wavefunction is not the essential object for Quantum Mechanics but one of convenient ways to express the action. We show that the Canonical Quantization scheme is considered to be a linear representation in complex variables of the consequences of this approach. This work is a kind of reformulation of Nelson’s stochastic quantization scheme and its variational formulation by Yasue. However, we believe that the present form of presentation will furnish possible way to deal with more complicated system such as Quantum Field theory, and also may suggest a new direction to discuss the origin of the Quantum Mechanics, for example, as a consequence of stochastic hidden noises for our space-time concept.

További információ: Ortvay Kollokvium – 2014 ősz