Dressed Photons to Revolutionize Modern Physics: Exploring Longitudinal Electromagnetic Waves and Off-Shell Quantum Fields

The book explains how, through a mathematical viewpoint, the underlying spatiotemporal vortex dynamics connect the dressed photon, the dark energy field, and the structure of the universe. The canonical equations of motion, which describe the time evolution of dynamical systems with Hamiltonian structure, play a key role in understanding these physical phenomena. In particular, the covariant form of equations of motion, where vortex tensors explicitly appear, corresponds to the transformed canonical equations of motion in the Eulerian representation.

This newly augmented view of the equations of motion presents a deeper understanding of the interconnectedness of different physical phenomena, which can enlighten graduate students, junior scientists, and industry engineers engaged or interested in this field.