The principles of a stochastic formulation of quantum theory

L. de la Peña-Auerbach

V. J. Lee

Zahid Zakir

Nelson's stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum.The unitary group of quantum mechanics is represented as the transformations of the systems of perturbing devices.It is argued that the physical spacetime has a stochastic nature and that quantum mechanics in Nelson's formulation correctly describes this stochasticity.

Vasil G. Yordanov

In this paper, we present a stochastic approach to relativistic quantum mechanics. We formulate the three fundamental principles of this theory and derive the Dirac equations based on them. This approach enables us to bring more insight into the nature of Dirac's spinors. Furthermore, we provide a physical interpretation of the stochastic optimal control theory of quantum mechanics.

Luigi Accardi, Igor Vasil'evich Volovich, Yun Gang Lu

Takeshi Kodama, Tomoi Koide C

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.