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Let F denote the Fock space for a free massless fermion field in two space‐time dimensions. If Q and Q 5 denote the charge and chiral charge operators, then F =⊕ n 1 , n 2 F n 1 , n 2 , where F n 1 , n 2 is the joint eigenspace of Q and Q 5 with corresponding eigenvalues n 1 and n 2 . The...
Representation theory of Lie algebras is called upon to develop a procedure for normalizing a dynamical system with two degrees of freedom in the neighborhood of an equilibrium when the Hamiltonian H ( x , y , X , Y ) in the coordinates ( x , y ) and their conjugate momenta ( X , Y ) is of the...
Three‐wave interaction in a possibly strongly inhomogeneous plasma was considered in Paper II. These results are now generalized in order to treat also time‐dependent periodic systems. The coupled mode equations as given in this paper are applicable to a very large class of unperturbed...
The conformal, homothetic, and isometric symmetries of all nontwisting type‐ N solutions are established. All solutions with λ allow at most the existence of two Killing vectors. All vacuum solutions, except the Robinson metric, permit maximally the existence of two (isometric and homothetic)...
A method is suggested for studying the Hamiltonian structure of the nonlinear partial differential equations that can be solved by the use of the spectral transform (soliton equations). The method is applied to a new hierarchy of N +1 coupled partial differential equations related to a...
For a massless conformally invariant scalar field, a class of solutions is obtained to the Einstein equations for which the geometry of the space‐time admits one timelike and two spacelike Killing vectors. The class of solutions admit plane‐symmetric and conformally flat solutions as special...
The purpose of this paper is to illustrate with a few concrete examples how the general formulas given in the preceding papers I–III may be used. We consider three different background plasmas: a homogeneous static magnetized plasma, a homogeneous magnetized plasma in an oscillating electric...
By an application of the geometrical techniques of Lie, Cohen, and Dickson it is shown that a system of differential equations of the form x ( r i i = F i (where r i >1 for every i =1,..., n ) cannot admit an infinite number of pointlike symmetry vectors. When r i = r for every i =1,..., n ,...
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