Two-dimensional two-particle quasipotential equation in a relativistic configuration representation

Partial integral quasipotential equations are formulated in the two-dimensional relativistic configuration representation. The explicit form of the partial Green functions of the two-dimensional quasipotential Logunov-Tavkhelidze equation is determined for an arbitrary value of the orbital quantum number. The equations obtained are applicable to describe in two-dimensional relativistic configuration representation bound states and scattering states of systems of two scalar particles of the same mass. A new formulation is proposed for two-dimensional relativistic scalar partial waves, mathematically expressed in terms of Legendre functions of the first and second kind with a half-integer subscript and a complex superscript. The asymptotic behavior and the non-relativistic limit of the relativistic partial waves and partial Green functions are obtained.

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