Section Guide 1. Prolegomena 2. Biographical Sketch 3. Epistemology 4. Textbook Ontology 1. PROLEGOMENA While both philosophers and historians almost always love truth and the search for truth, and both often carry out extensive research, there can be noticeable differences when historians write about the history of philosophy and when philosophers write about it. Philosophers often look at the past with categories and interests taken from the present or at the least from the recent past, but many historians, especially those who love research for its own sake, will try to look at the past from a perspective either from that period or from even earlier. Both camps look for roots, but view them with different lenses and presupposi tions. This prolegomena has been added to prepare some philosophers for what will hopefully only be the mildest of shocks, for seeing the history of philosophy in a way which does not treat what is recent or latest as best, but which loves the context of ideas for its own sake, a context which can be very foreign to contemporary likes and dislikes. To be sure, we historians can deceive ourselves as easily as philosophers, but we tend to do so about different things.

This is a textbook on stochastic quantization which was originally proposed by G. Parisi and Y. S. Wu in 1981 and then developed by many workers. I assume that the reader has finished a standard course in quantum field theory. The Parisi-Wu stochastic quantization method gives quantum mechanics as the thermal-equilibrium limit of a hypothetical stochastic process with respect to some fictitious time other than ordinary time. We can consider this to be a third method of quantization; remarkably different from the conventional theories, i. e, the canonical and path-integral ones. Over the past ten years, we have seen the technical merits of this method in quantizing gauge fields and in performing large numerical simulations, which have never been obtained by the other methods. I believe that the stochastic quantization method has the potential to extend the territory of quantum mechanics and of quantum field theory. However, I should remark that stochastic quantization is still under development through many mathematical improvements and physical applications, and also that the fictitious time of the theory is only a mathematical tool, for which we do not yet know its origin in the physical background. For these reasons, in this book, I attempt to describe its theoretical formulation in detail as well as practical achievements.

Section Guide 1. Prolegomena 2. Biographical Sketch 3. Epistemology 4. Textbook Ontology 1. PROLEGOMENA While both philosophers and historians almost always love truth and the search for truth, and both often carry out extensive research, there can be noticeable differences when historians write about the history of philosophy and when philosophers write about it. Philosophers often look at the past with categories and interests taken from the present or at the least from the recent past, but many historians, especially those who love research for its own sake, will try to look at the past from a perspective either from that period or from even earlier. Both camps look for roots, but view them with different lenses and presupposi tions. This prolegomena has been added to prepare some philosophers for what will hopefully only be the mildest of shocks, for seeing the history of philosophy in a way which does not treat what is recent or latest as best, but which loves the context of ideas for its own sake, a context which can be very foreign to contemporary likes and dislikes. To be sure, we historians can deceive ourselves as easily as philosophers, but we tend to do so about different things.