A Lagrangian formalism of scalar fields is considered and a new concept of “connection” is introduced. By this a gauge-theoretic understanding of the Sato theory on the K.-P. system is obtained. Our gauge group ˜{
G}
− is the group consisting of pseudo-differential operators of non-positive orders with certain growth conditions. Then it can be concluded that the space
R* of elements of ˜{
G}
− giving solutions of the K.-P. system defines a flat
R*-connection which we call the K.-P. connection. This connection can be regarded as a special gauge field.
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