Abstract
In the first part of the paper, the so-called generalized position operators proposed by Fleming are investigated. Compact expressions for these operators are given (a so-called transversal angular momentum operator is introduced for this purpose), and the properties of their algebraic structure are discussed. The second part is devoted to multiparticle eigenvectors for two of the three kinds of the position operators. The obtained solutions permit one to separate property the global motion of a physical system from its internal motions. The obtained internal variables are relativistic counterparts of relative velocities. The considerations are carried out in the general framework of quantum field theory and are based on the reconstruction theorem of the axiomatic quantum field theory. This also allows us to use the results for interacting systems. The discussion of Lorentz covariance of the localized states is carried out.
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