β Scribed by P.M Mathews; M Lakshmanan
No coin nor oath required. For personal study only.
A systematic study is made of the plane wave modes of a nonlinear c-number field (h$* model) and interesting features of the behavior of such fields, which do not seem to have been observed before, are brought out. These relate to the case h < 0, wherein there are different regimes characterized by different kinds of elliptic-function forms for the waves. We show that when the amplitude of the elliptic function waves approaches critical values corresponding to "phase transition" from one regime to another, the energy density in the field increases without limit (though the amplitude is finite). In two of the regimes which are "tachyonic" in nature, there are frozen wave modes which are spatially periodic but time independent. These turn out however to be unstable against perturbations. FinaIly we observe that in one of these regimes there exist a lower bound on the energy density in the wave field. The case of fields with higher nonlinearities is briefly considered.
π SIMILAR VOLUMES
We consider a description of membranes by (2, 1)-dimensional field theory, or alternatively a description of irrotational, isentropic fluid motion by a field theory in any dimension. We show that these Galileo-invariant systems, as well as others related to them, admit a peculiar diffeomorphism symm