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Here we study a new kind of linear integral equations for a relativisticquantum-mechanical two-particle wave function $\psi(x_1,x_2)$, where $x_1,x_2$are spacetime points. In the case of retarded interaction, these integralequations are of Volterra-type in the in the time variables, i.e., they involvea time integration from 0 to $t_i = x_i^0,~i=1,2$. They are interesting notonly in view of their applications in physics, but also because of thefollowing mathematical features: (a) time and space variables are moreinterrelated than in normal time-dependent problems, (b) the integral kernelsare singular, and the structure of these singularities is non-trivial, (c) theyfeature time delay. We formulate a number of examples of such equations forscalar wave functions and prove existence and uniqueness of solutions for them.We also point out open mathematical problems.

A new class of Volterra-type integral equations from relativistic quantum physics