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The limiting process is developed, stressing the simplicity of the null‐plane formulation. A SU(2) ‘‘dual’’ invariance for the dynamical variables is made explicit. The symmetry is not satisfied by the field strengths.
We consider the general form of the finite difference approximation to the Dirac (Weyl) Hamiltonian on a lattice and investigate systematically the dependence on symmetry of the number of particles described by it. To a lattice with given symmetry, expressed by its crystallographic space group,...
Starting from the oscillator representation of the three‐dimensional Lorentz algebra so(2,1), we build a Lie algebra of second‐order differential operators which realizes all series of self‐adjoint irreducible representations. The choice of the common self‐adjoint extention over a...
After defining a generalized Weyl correspondence, we give some general results. These are presented as comments on a theorem. They mainly refer to the finite‐dimensional, unbounded, and non‐self‐adjoint cases.
A new family of exact solutions of the stationary axially symmetric vacuum Einstein equations is presented. The internal symmetries, SL(2,R) rotation, and duality of parametrization, are combined to construct a Bäcklund transformation. For the special ansatz of the field equations, the Bäcklund...
The results of the theory of complexified V 4 ’s which admit a null string are reexamined by using systematically the Bianchi identities. The formal reasons which permit the integration of the G μν=0 equations to one differential constraint in the case of the H H structures are exhibited....
Simple ideas based on quantum chromodynamics suggest that the strong nuclear force might possess a long‐range van der Waals component. Such a component, if it exists, would be most apparent in low‐energy interactions between pairs of hadrons, at least one of which is neutral. In this article,...
We prove that solutions of the factorization equations for S matrices with Z n symmetry can be given in terms of theta functions. We present a class of vertex models based on A ‐symmetric S matrices ( A being an abelian group) as natural generalizations of the Baxter model. The mapping of these...
The norms of the Bethe‐ansatz eigenstates of the chiral‐invariant Gross–Neveu Hamiltonian are calculated.
Examples of classes of nonlinear representations of Lie groups are given. Nonlinear representations which are a perturbation of a unitary representation of the discrete series of SU(1,1) are then proved to be formally linearizable.
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