VARIATIONAL APPROACH TO THE DYNAMICS OF QUANTUM FIELDS

摘要

In the summer of 1995, Dominique Vautherin came tc Kyoto and stayed three months at the Yukawa Institute of Kyoto University where he delivered a series of very informal, pedagogical lectures on the application of variational methods to quantum field theories. This initiated our long lasting enjoyable collaboration on the subject and Yasuhiko Tsue joined the force later Throughout this collaboration Vautherin was always enthusiastic to explore new physics problems and always came up with new innovative ideas, much of which I suspect have origins in his expertise in nuclear many-body theory. We are very sorry that this fruitful collaboration with Vautherin came to end so soon by his untimely death and that we are no longer able to be inspired by his deep physics insights, charmed by his elegance, and most of all cheered up by his very warm p resence. I like to dedicate these lectures to the memory of Dominique Vautherin f om whom I learned most of the material presented below. First, I like to say a few words about physics motivations of our works. In recent years, several authors have constructed non-trivial time-dependent solutions of classical field equations of effective meson fields. Such solutions are relevant in considering the fate of defects which might be produced in dynamical order-disorder phase transitions in ultrarelativistic nucleus-nucleus collisions or in the evolution of very early universe. We like to study the effect of quantum fluctuations which has been ignored in these classical analyses. We may consider the classical solution as a collective mode of underlying microscopic degrees of freedom. It is well-known in nuclear many-body theory that the internal microscopic motions of nucleons are influenced by the motion of the nuclear mean field such as rotation or vibration. One may expect similar effects would arise in the field theory.