Renormalized nonperturbative fermion model in covariant light-front dynamics

Karmanov, V. A.; Mathiot, J.-F.; Smirnov, A. V.

doi:10.1103/physrevd.69.045009

Cited by 24 publications

(72 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since some integrals over dx diverge logarithmically at x = 0 and/or x = 1, we also introduce (where it is needed) an infinitesimal positive cutoff ǫ, assuming that x may belong to the intervals ǫ < x < 1 − ǫ and 1 + ǫ < x < +∞. The corresponding analytical expressions for the functions A(p 2 ), B(p 2 ), C(p 2 ), and C f c were found in Ref [7]:…”

Section: Regularization With Rotationally Non-invariant Cutoffsmentioning

confidence: 99%

See 1 more Smart Citation

Regularization of the fermion self-energy and the electromagnetic vertex in the Yukawa model within light-front dynamics

2007

Self Cite

View full text Add to dashboard Cite

In light-front dynamics, the regularization of amplitudes by traditional cutoffs imposed on the transverse and longitudinal components of particle momenta corresponds to restricting the integration volume by a non-rotationally invariant domain. The result depends not only on the size of this domain (i.e., on the cutoff values), but also on its orientation determined by the position of the light-front plane. Explicitly covariant formulation of light front dynamics allows us to parameterize the latter dependence in a very transparent form. If we decompose the regularized amplitude in terms of independent invariant amplitudes, extra (non-physical) terms should appear, with spin structures which explicitly depend on the orientation of the light front plane. The number of form factors, i.e., the coefficients of this decomposition, therefore also increases. The spin-1/2 fermion self-energy is determined by three scalar functions, instead of the two standard ones, while for the elastic electromagnetic vertex the number of form factors increases from two to five. In the present paper we calculate perturbatively all these form factors in the Yukawa model. Then we compare the results obtained in the two following ways: (i) by using the light front dynamics graph technique rules directly; (ii) by integrating the corresponding Feynman amplitudes in terms of the light front variables. For each of these methods, we use two types of regularization: the transverse and longitudinal cutoffs, and the Pauli-Villars regularization. In the latter case, the dependence of amplitudes on the light front plane orientation vanishes completely provided enough Pauli-Villars subtractions are made.

show abstract

Section: Regularization With Rotationally Non-invariant Cutoffsmentioning

confidence: 99%

“…Note that without adding new, ω-dependent, counterterms in the interaction Hamiltonian, this dependence is not killed by the standard renormalization. The renormalization recipe must be therefore modified [7].…”

Section: Regularization With Rotationally Non-invariant Cutoffsmentioning

confidence: 99%

Regularization of the fermion self-energy and the electromagnetic vertex in the Yukawa model within light-front dynamics

2007

Self Cite

View full text Add to dashboard Cite

show abstract

“…More recent calculations [24,82] use PV regularization. The one-photon truncation of the dressed electron state has also been computed by Karmanov et al [145,18]. The dressed-photon state has also been investigated [108]; the appropriate PV regularization has been found to enforce a zero eigenmass for the photon.…”

Section: Quantum Electrodynamicsmentioning

confidence: 99%

“…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.…”

Section: Yukawa Theorymentioning

confidence: 99%

Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

View full text Add to dashboard Cite

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, φ 4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

show abstract

“…Truncated LF Fock space decomposition was applied in [6] to nonperturbative study the large α QED. Recently, the Fock decomposition, incorporating first three Fock sectors, was used for nonperturbative renormalization in a scalar model [7] and, with two sectors, -in Yukawa model [8,9] and in gauge theory [9].…”

Section: Introductionmentioning

confidence: 99%

Many-body Fock sectors in Wick–Cutkosky model

Hwang

Karmanov

2004

Nuclear Physics B

View full text Add to dashboard Cite

In the model where two massive scalar particles interact by the ladder exchanges of massless scalar particles (Wick-Cutkosky model), we study in light-front dynamics the contributions of different Fock sectors (with increasing number of exchanged particles) to full normalization integral and electromagnetic form factor. It turns out that two-body sector always dominates. At small coupling constant α ≪ 1, its contribution is close to 100%. It decreases with increase of α. For maximal value α = 2π, corresponding to the zero bound state mass, two-body sector contributes to the normalization integral 64%, whereas the three-body contribution is 26% and the sum of all higher contributions from four-to infinite-body sectors is 10%. Contributions to the form factor from different Fock sectors fall off faster for asymptotically large Q 2 , when the number of particles in the Fock sectors becomes larger. So, asymptotic behavior of the form factor is determined by the two-body Fock sector.

show abstract

Renormalized nonperturbative fermion model in covariant light-front dynamics

Cited by 24 publications

References 23 publications

Regularization of the fermion self-energy and the electromagnetic vertex in the Yukawa model within light-front dynamics

Regularization of the fermion self-energy and the electromagnetic vertex in the Yukawa model within light-front dynamics

Nonperturbative light-front Hamiltonian methods

Many-body Fock sectors in Wick–Cutkosky model

Contact Info

Product

Resources

About