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 lightfront dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane ω•x = 0 defined by a light-like four-vector ω. 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 Relativistic Description of Two-and Three-Body Systems in Nuclear Physics", ECT*, October 19-23 2009

Ab initiononperturbative calculation of physical observables in light-front dynamics: Application to the Yukawa model

“…In addition, the magnitude of Z ω (x) is reasonably smaller than that calculated in the f + f b + f bb truncated Fock space. The fact that g 03 (x) and Z ω (x) are close to con- stants is not a specific property of the Yukawa model, since we already encountered similar features in our studies of the scalar model [6]. In contrast to the latter, where we incorporated particle-antiparticle loop contributions as well, we reproduced the property g 03 (x) ≈ const in the Yukawa model within the quenched approximation.…”

Nonperturbative solution of scalar Yukawa model in two- and three-body Fock space truncations

“…This was done in Refs. [17] (within the scalar Yukawa model) and [7] (within the spinor Yukawa model in the quenched approximation, i.e., neglecting fermion-antifermion loop contributions). The results of numerical nonperturbative calculations of the on-energy-shell two-body vertex function Γ…”

Renormalized Light Front Hamiltonian in the Pauli-Villars Regularization

“…The generalization of this method allowing to consider the states with infinite number of quanta was proposed in [34,35] (it is the so called LF coupled-cluster (LFCC) method). The PV regularization was used, in particular, in Covariant Light Front Dynamics (CLFD) approach [36][37][38] where the truncation of LF Fock basis of states and the corresponding renormalization procedure within covariant formulation on the LF were used.…”