Quantization and Gauge Field

Abstract

We have discussed in the previous section that relativistic generalization of the stochastic quantization procedure and quantization of a Fermi field can be achieved if we incorporate Brownian motion processes in the internal space also apart from that in the external space. That means, after quantization for an observational procedure we can think of the mean position of the particle q μ in the external observable space with a stochastic extension determined by the internal stochastic variable O μ This is the basic premise of Prugovecki’s stochastic quantum mechanics ((1986)).