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We carry out a constructive review of non-standard solutions of relativistic wave equations. Such solutions are obtained via splitting of relativistic wave equations written in spinor form. All these solutions are also solutions of the Dirac equation and are non-standard because they involve higher-order spinors. The main finding is that non-standard solutions describe decaying states.
Classical results and recent developments on the theoretical description of elementary particles with continuous spin are reviewed. At free level, these fields are described by unitary irreducible representations of the isometry group (either Poincar
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining po
On the basis of the three fundamental principles of (i) Poincar{e} symmetry of space time, (ii) electromagnetic gauge symmetry, and (iii) unitarity, we construct an universal Lagrangian for the electromagnetic interactions of elementary vector partic
We explicitly write dowm integral formulas for solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded -- neither highest nor lowest weight -- $gtsl_{n+1}$-modules. The formulas are closely related to WZNW model at a rational level.
We show that reductions of KP hierarchies related to the loop algebra of $SL_n$ with homogeneous gradation give solutions of the Darboux-Egoroff system of PDEs. Using explicit dressing matrices of the Riemann-Hilbert problem generalized to include a