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-defined Fock components. In order to control the convergence of this expansion, we advocate the use of the covariant formulation of light-front dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane $ω\cd x=0$ defined 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 field-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 two-body 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 effective field theories like chiral perturbation theory in the baryonic sector.

17 pages, 19 figures "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ECT*, October 19-23 2009

References in corpus (18)

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• Application of Pauli-Villars regularization and discretized light-cone quantization to a single-fermion truncation of Yukawa theory
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• Nonperturbative renormalization in a scalar model within Light-Front Dynamics
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• Restoration of the chiral limit in Pauli-Villars-regulated light-front QED
• UV and IR behaviour in QFT and LCQFT with fields as Operator Valued Distributions:Epstein and Glaser revisited
• The nucleon wave function in light-front dynamics
• Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics
• Quantum Fields as Operator Valued Distributions and Causality

Cited by in corpus (4)

• Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model
• Nonperturbative solution of scalar Yukawa model in two- and three-body Fock space truncations
• Renormalized Light Front Hamiltonian in the Pauli-Villars Regularization
• Abnormal Bound Systems