Local Quantum Mechanics and Lorentz Transformation

The transformation property under the Poincare group of the recently proposed local quantum mechanics is expressed by depending on a correspondence with the quantum field theory in terms of ten generators of infinitesimal transformations in the state-vector space for a simple example, in the continuum approximation which represents the finite momentum degree of freedom by a continuous density function. They "do not generate the representation of the Poincare group but seven of them generate the unitary representation of the group composed of the 4-dimensional translation and the 3-dimensional rotation around a universal timelike vector. The deviation from the Lorentz invarian ce is due to the finiteness of the momentum degree of freedom of the system and considered to have observable effects in ultrahigh energy phenomena.