ALGEBRAIC STRUCTURE OF QUANTUM FLUCTUATIONS

On the basis of the existence of second and third moments of fluctuati ons, we prove a theorem about the Lie-algebraic structure of fluctuati on operators. This result gives insight into the quantum character of fluctuations. We illustrate the presence of a Lie algebra of fluctuati on operators in a model of the anharmonic crystal, and show the depend ence of the Lie-algebra structure on the fine structure of the fluctua tion operator algebra. The result is also applied to construct the nor mal Goldstone mode in the ideal Bose gas for Bose-Einstein condensatio n.