1,483 research outputs found
Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model
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.Comment: 22 pages, 16 figure
Systematic renormalization scheme in light-front dynamics with Fock space truncation
Within the framework of the covariant formulation of light-front dynamics, we
develop a general non-perturbative renormalization scheme based on the Fock
decomposition of the state vector and its truncation. The counterterms and bare
parameters needed to renormalize the theory depend on the Fock sectors. We
present a general strategy in order to calculate these quantities, as well as
state vectors of physical systems, in a truncated Fock space. The explicit
dependence of our formalism on the orientation of the light front plane is
essential in order to analyze the structure of the counterterms. We apply our
formalism to the two-body (one fermion and one boson) truncation in the Yukawa
model and in QED, and to the three-body truncation in a scalar model. In QED,
we recover analytically, without any perturbative expansion, the
renormalization of the electric charge, according to the requirements of the
Ward identity.Comment: 32 pages, 14 figures, submitted in Phys. Rev.
Recent developments in light-front dynamics
Recent results on relativistic few body systems, obtained in the framework of
light-front dynamics, are briefly reviewed. The following subjects are
discussed: two scalar bosons with ladder and cross ladder kernel; two fermions
with OBE kernel; relativistic scattering (elastic and inelastic); three bosons
and fermions with zero-range interaction; many-body contributions.Comment: 5 pages, 4 figures, to appear in the proceedings of the 19th European
Conference on Few-Body Problems in Physics, Groningen, The Netherlands,
August 23-27, 200
Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space
Within the covariant formulation of light-front dynamics, we calculate the
state vector of a physical fermion in the Yukawa model. The state vector is
decomposed in Fock sectors and we consider the first three ones: the single
constituent fermion, the constituent fermion coupled to one scalar boson, and
the constituent fermion coupled to two scalar bosons. This last three-body
sector generates nontrivial and nonperturbative contributions to the state
vector, which are calculated numerically. Field-theoretical divergences are
regularized using Pauli-Villars fermion and boson fields. Physical observables
can be unambiguously deduced using a systematic renormalization scheme we have
developed previously. As a first application, we consider the anomalous
magnetic moment of the physical fermion.Comment: 24 pages, 16 figure
Critical stability of few-body systems
When a two-body system is bound by a zero-range interaction, the
corresponding three-body system -- considered in a non-relativistic framework
-- collapses, that is its binding energy is unbounded from below. In a paper by
J.V. Lindesay and H.P. Noyes it was shown that the relativistic effects result
in an effective repulsion in such a way that three-body binding energy remains
also finite, thus preventing the three-body system from collapse. Later, this
property was confirmed in other works based on different versions of
relativistic approaches. However, the three-body system exists only for a
limited range of two-body binding energy values. For stronger two-body
interaction, the relativistic three-body system still collapses.
A similar phenomenon was found in a two-body systems themselves: a
two-fermion system with one-boson exchange interaction in a state with zero
angular momentum J=0 exists if the coupling constant does not exceed some
critical value but it also collapses for larger coupling constant. For a J=1
state, it collapses for any coupling constant value. These properties are
called "critical stability". This contribution aims to be a brief review of
this field pioneered by H.P. Noyes.Comment: 20 pages, 7 figures, 1 tabl
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