Geometric View on Photon-like Objects

This book aims to summarize in a consistent way the authors' results in attempting to build spatially finite and time-stable models of photon-like objects through extending Maxwell vacuum equations to local energy-momentum exchange relations and making use of modern differential geometry. In particular, we interpret dynamically Frobenius integrability theory of distributions on manifolds through an appropriate $\varphi$-extension along $p$-vector fields of the classical Lie derivative, and give interaction interpretation of the nonintegrability of subdistributions of an integrable distribution recognizing physically these subdistributions as time-stable subsystems of the field object considered and formally presented by the integrable distribution. The space-time propagation of our photon-like object is, of course, along appropriate symmetry of the representing distribution.