Exploring straight infinite Wilson lines towards formulating a new classical theory for gluodynamics

We develop a new classical action that in addition to MHV vertices contains also N^kMHV vertices, where 1 = k = n - 4 with n the number of external legs. The lowest order vertex is the four-point MHV vertex - there is no three point vertex and thus the amplitude calculation involves fewer diagrams than in the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action. The action is obtained by a canonical transformation of the Yang-Mills action in the light-cone gauge, where the field transformations are based on Wilson line functionals.