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Nonperturbative renormalization in light-front dynamics and applications

Abstract : We present a general framework to calculate the properties of relativistic compound systems from the knowledge of an elementary Hamiltonian. Our framework provides a well-controlled nonperturbative calculational scheme which can be systematically improved. The state vector of a physical system is calculated in light-front dynamics. From the general properties of this form of dynamics, the state vector can be further decomposed in well-dened Fock components. In order to control the convergence of this expansion, we advocate the use of the covariant formulation of lightfront dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane omega . x = 0 dened by a light-like four-vector omega. This enables us to control any violation of rotational invariance due to the truncation of the Fock expansion. We then present a general nonperturbative renormalization scheme in order to avoid eld-theoretical divergences which may remain uncancelled due to this truncation. This general framework has been applied to a large variety of models. As a starting point, we consider QED for the twobody Fock space truncation and calculate the anomalous magnetic moment of the electron. We show that it coincides, in this approximation, with the well-known Schwinger term. Then we investigate the properties of a purely scalar system in the three-body approximation, where we highlight the role of antiparticle degrees of freedom. As a non-trivial example of our framework, we calculate the structure of a physical fermion in the Yukawa model, for the three-body Fock space truncation (but still without antifermion contributions). We finally show why our approach is also well-suited to describe eective eld theories like chiral perturbation theory in the baryonic sector.
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Jean-Francois Mathiot, A.V. Smirnov, N.A. Tsirova, V.A. Karmanov. Nonperturbative renormalization in light-front dynamics and applications. Few-Body Systems, Springer Verlag, 2011, 49, pp.183-203. ⟨10.1007/s00601-010-0188-3⟩. ⟨in2p3-00528602⟩

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