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Feynman diagrams and interaction rules of wave‐wave scattering processes
Author(s) -
Hasselmann K.
Publication year - 1966
Publication title -
reviews of geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 8.087
H-Index - 156
eISSN - 1944-9208
pISSN - 8755-1209
DOI - 10.1029/rg004i001p00001
Subject(s) - feynman diagram , physics , collision , nonlinear system , antiparticle , classical mechanics , scattering , lattice (music) , perturbation (astronomy) , statistical physics , quantum mechanics , quantum electrodynamics , theoretical physics , computer security , computer science , acoustics , lepton , electron
The energy transfer due to weak nonlinear interactions in random wave fields is reinterpreted in terms of a hypothetical ensemble of interacting particles, antiparticles, and virtual particles. In the particle picture, the interactions can be conveniently described by Feynman diagrams, which may be regarded either as branch diagrams of the perturbation expansion or as collision diagrams. The derivation of the transfer expressions can then be reduced to a few general rules for the construction of the diagrams and the associated collision cross sections. The representation follows closely the standard treatment of nonlinear lattice vibrations, but the particle picture differs from the usual phonon interpretation of lattice waves. It has the unrealistic property that the energies and number densities of antiparticles are negative. This is offset by simpler interaction rules and a closer correspondence between the perturbation graphs and collision diagrams. The method is illustrated for scattering processes in the oceanic wave guide involving surface and internal gravity waves, horizontal currents (turbulence), seismic waves, and bottom irregularities.