We have recently solved the inverse scattering problem for oneparameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev Petviashvili (dKP) equation. We showed, in particu...

We present an elementary method to obtain Green’s functions in non-perturbative quantum field theory in Minkowski space from calculated Green’s functions in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes is many times unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore ...

1. Introductory remarks 1 2. Energy and area 3 3. Exact Lagrangian submanifolds and the non-squeezing theorem 7 4. Sobolev spaces 9 5. The linear Cauchy–Riemann operator 20 5.1. Proof of the Calderón–Zygmund Theorem for p , 2 26 6. Local properties of J-holomorphic curves 30 6.1. Smoothness 31 6.2. The Carleman Similarity Principle and its applications 35 6.3. Isolation of intersection points a...