Green’s functions of relativistic oscillators with generalized Dunkl derivative: the (1+1)-dimensional case

Abstract The Green’s functions for relativistic oscillators with spin-0 and spin-1/2, within the framework of a new generalization of the Dunkl derivative with three parameters, are calculated using the path integral approach. For simplicity, this derivative is reformulated to depend on only two parameters. As a result, the energy eigenvalues and their corresponding wave functions are determined in both cases as functions of the three deformed parameters. In the limiting cases of the deformed parameters, the standard Dunkl derivative system is recovered, even in the absence of the Dunkl parameters.