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

Abstract

We present a coherent and operational strategy to calculate, in a nonperturbative way, physical observables in light-front dynamics. This strategy is based on the decomposition of the state vector of any compound system in Fock components, and on the covariant formulation of light-front dynamics, together with the so-called Fock sector dependent renormalization scheme. We apply our approach to the calculation of the electromagnetic form factors of a fermion in the Yukawa model, in the nontrivial three-body Fock space truncation, for rather large values of the coupling constant. We find that, once the renormalization conditions are properly taken into account, the form factors do not depend on the regularization scale, when the latter is much larger than the physical masses. We then extend the Fock space by including antifermion degrees of freedom.

Basis light-front quantization approach to positronium

“…The main challenge is the development and implementation of a non-perturbative renormalization scheme, such as the Fock sector dependent scheme of Refs. [39,40]. The recent successful renormalization of the free electron problem in BLFQ [11] with a dynamical photon in the basis suggests the possibility of "embedding" the renormalized, physical electron into the positronium system [43].…”

Nonperturbative light-front Hamiltonian methods

“…Closely following this work, there was a sequence of investigations [144,145,146,19,147] within the context of covariant light-front dynamics and eventually employing PV regularization and sectordependent renormalization. This work included computation of the anomalous magnetic moment [19] and even the electromagnetic form factors [147] of the fermion dressed by one or two bosons.…”

“…Yukawa theory also offers the opportunity to study an unquenched theory and the associated renormalizations of the charge and scalar mass, something for which the unstable scalar Yukawa theory cannot be used. This aspect is largely unexplored at present, although some preliminary work has been done [94,147]. Applications to modeling of scalar meson exchange in nuclear physics are quite limited, given that accurate phenomenology requires a more sophisticated interaction [149].…”

“…This work included computation of the anomalous magnetic moment [19] and even the electromagnetic form factors [147] of the fermion dressed by one or two bosons. Dependence on the cutoff is eliminated to within numerical accuracy.…”

Scattering in time-dependent basis light-front quantization

“…(Hence, we adopt physical values for the electron mass and charge.) Renormalization within the BLFQ framework is possible, via a sectordependent scheme [43,[47][48][49]. For an application, see [49], in which the scheme is implemented for the QED Hamiltonian; the resulting electron anomalous magnetic moment agrees with the Schwinger value to within 1%.…”