Basic Ideas of Stochastic Quantization

Steven M. Moore

Michio Masujima

Takeshi Kodama, Tomoi Koide C

The well-known hydrodynamical representation of the Schrödinger equation is reformulated by extending the idea of Nelson-Yasue's stochastic variational method. The fluid flow is composed by the two stochastic processes from the past and the future, which are unified naturally by the principle of maximum entropy. We show that this formulation is easily applicable to the quantization of scalar fields.

Kunio Yasue

The stochastic quantization procedure, proposed by Nelson, is further developed to include the problem of field quantization. To maintain the mathematical rigor in treating infinitely many degrees of freedom, basic notions of the nonstandard analysis are adopted. As an application of the present method, a quantum mechanical description of dissipatively interacting fields, such as the laser electric field in the lossy cavity, is investigated.

Kunio Yasue