Renormalized Poincaré algebra for effective particles in quantum field theory

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Using an expansion in powers of an infinitesimally small coupling constant g, all generators of the Poincaré group in local scalar quantum field theory with interaction term g ϕ³ are expressed in terms of annihilation and creation operators aλ and a†λ that result from a boost-invariant renormalization group procedure for effective particles. The group parameter λ is equal to the momentum-space width of form factors that appear in vertices of the effective-particle Hamiltonians, Hλ. It is verified for terms order 1, g, and g², that the calculated generators satisfy required commutation relations for arbitrary values of λ. One-particle eigenstates of Hλ are shown to properly transform under all Poincaré transformations. The transformations are obtained by exponentiating the calculated algebra. From a phenomenological point of view, this study is a prerequisite to construction of observables such as spin and angular momentum of hadrons in quantum chromodynamics.