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A Possible Way for Constructing Generators of the Poincaré Group in Quantum Field Theory

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Abstract

Starting from the instant form of relativistic quantum dynamics for a system of interacting fields, where amongst the ten generators of the Poincaré group only the Hamiltonian and the boost operators carry interactions, we offer an algebraic method to satisfy the Poincaré commutators.We do not need to employ the Lagrangian formalism for local fields with the Nöether representation of the generators. Our approach is based on an opportunity to separate in the primary interaction density a part which is the Lorentz scalar. It makes possible apply the recursive relations obtained in this work to construct the boosts in case of both local field models (for instance with derivative couplings and spins ≥ 1) and their nonlocal extensions. Such models are typical of the meson theory of nuclear forces, where one has to take into account vector meson exchanges and introduce meson-nucleon vertices with cutoffs in momentum space. Considerable attention is paid to finding analytic expressions for the generators in the clothed-particle representation, in which the so-called bad terms are simultaneously removed from the Hamiltonian and the boosts. Moreover, the mass renormalization terms introduced in the Hamiltonian at the very beginning turn out to be related to certain covariant integrals that are convergent in the field models with appropriate cutoff factors.

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Authors and Affiliations

  1. Institute for Theoretical Physics, National Research Center “Kharkov Institute of Physics and Technology”, 1 Akademicheskaya St., 61108, Kharkiv, Ukraine

    A. V. Shebeko

  2. Institute of Electrophysics and Radiation Technologies, NAS of Ukraine, 28 Chernyshevsky St., P.O. Box 8812, 61002, Kharkiv, Ukraine

    P. A. Frolov

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  1. A. V. Shebeko
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  2. P. A. Frolov
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Correspondence to A. V. Shebeko.

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In memory of Mikhail Shirokov, the excellent scientist and modest person

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Shebeko, A.V., Frolov, P.A. A Possible Way for Constructing Generators of the Poincaré Group in Quantum Field Theory. Few-Body Syst 52, 125–164 (2012). https://doi.org/10.1007/s00601-011-0262-5

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