プラズマ理論の技法支援論文 C.不変測度

抄録

To develop a statistical theory, one has to define a probability density on the phase space of ensemble. The measure of the space, then, must be invariant against the map (flow) representing the dynamics. This property is warranted by the Liouville theorem in the canonical Hamitonian dynamics. For some infinite dimension dynamics, we can construct an ”invariant measure” by an appropriate eigenfunction expansion of fields, which provides a basis to construct statistical mechanical theory of the fields.