Geometrical aspects of the K

A twistor Cech cohomological characterization of mixed frequency zero rest-mass elds is developed. Using a Cech form of the cup product we derive an expression for the symplectic product of two real mixed frequency scalar elds in terms of a single vertex diagram. An expression for the frequency splitting complex structure of quantum eld theory is derived, and presented by its action on a mixed frequency twistor function. These results are applied to give a twistor contour integral that expresses the positive deenite norm on the space of mixed frequency elds in terms of the associated twistor functions.