Relativistic Ŝ-matrix formulation in one dimension for particles of spin-s (s = 0, 1/2)

Abstract In quantum scattering theory, the time evolution of a physical system can be described as a series of unitary transformations. The operator of this transformation will be denoted S ̂ $\hat{\boldsymbol{S}}$ ; the corresponding matrix is the Ŝ -matrix (scattering matrix). This last object contains all the information on the broadcast process associated with the operator S ̂ $\hat{\boldsymbol{S}}$ The present work has two objectives: To develop the one-dimensional formalism of the scattering matrix of relativistic particles of spin-s ( s = 0, 1/2) in the presence of a localized electromagnetic field on the one hand and on the other hand to analyze the solutions of the problem of scattering states of relativistic particles of spin-s in interaction with some localized scalar potentials via the S ̂ $\hat{S}$ -matrix formalism.