Generalized Hamiltonians, Functional Integration and Statistics of Continuous Fluids and Plasmas*

Generalized Hamiltonian formalism including generalized Poisson brackets and Lie-Poisson brackets is presented in Section II. Gyroviscous magnetohydrodynamics is treated as a relevant example in Euler and Clebsch variables. Section III is devoted to a short review of functional integration containing the definition and a discussion of ambiguities and methods of evaluation. The main part of the contribution is given in Sect. IV, where some of the content of the previous sections is applied to Gibbs statistics of continuous fluids and plasmas. In particular, exact fluctuation spectra are calculated for relevant equations in fluids and plasmas.