Note on Fluctuations

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Abstract
We treat three standard problems of the nonrelativistic quantum theory by a Brownian-motion method devised by Sokolov and Tumanov. In all three cases, the commutation (Poisson bracket) relations for the particle's dynamical variables are deduced from the corresponding relations for the components of the fluctuating electromagnetic field. In addition, the particle ground-state energy is determined by the zero-temperature vacuum fluctuations of the field. The ground-state energy includes the lowest-order radiative correction, although the calculation makes no use of traditional perturbation theory or mass renormalization. If the vacuum radiation temperature is high, the energy of the particle goes to its equipartition value.

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