Abstract
The technique of projecting the four-dimensional two-body Bethe–Salpeter equation onto the three-dimensional Light-Front hypersurface, combined with the quasi-potential approach, is briefly illustrated, by placing a particular emphasis on the relation between the projection method and the effective dynamics of the valence component of the Light-Front wave function. Some details on how to construct the Fock expansion of both (a) the Light-Front effective interaction and (b) the electromagnetic current operator, satisfying the proper Ward–Takahashi identity, will be presented, addressing the relevance of the Fock content in the operators living onto the Light-Front hypersurface. Finally, the generalization of the formalism to the three-particle case will be outlined.
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References
Dirac P.A.M.: Forms of relativistic dynamics. Rev. Mod. Phys. 21, 392 (1949)
Leutwyler H., Stern J.: Relativistic dynamics on a null plane. Ann. Phys. 112, 94 (1978)
Biernat, E.P., Klink, W.H., Schweiger, W.: Point-form Hamiltonian dynamics and applications. arXiv:1008.0244v1
Keister B.D., Polyzou W.N.: Relativistic Hamiltonian dynamics in nuclear and particle physics. Adv. Nucl. Phys. 20, 225 (1991)
Carbonell J., Desplanques B., Karmanov V.A., Mathiot J.F.: Explicitly covariant light front dynamics and relativistic few body systems. Phys. Rep. 300, 215 (1998)
Brodsky S.J., Pauli H.-C., Pinsky S.S.: Quantum chromodynamics and other theories on the light-cone. Phys. Rep. 301, 299 (1998)
Perry R.J., Harindranath A., Wilson K.G.: Light front Tamm-Dancoff field theory. Phys. Rev. Lett. 65, 2959 (1990)
Lev F.M., Pace E., Salmè G.: Electromagnetic and weak current operators for interacting systems within the Front-form dynamics. Nucl. Phys. A 641, 229 (1998)
Gross F.: Relativistic quantum mechanics and field theory. Wiley, New York (1993)
Pauli H.-C.: On confinement in a light-cone Hamiltonian for QCD. Eur. Phys. J. C 7, 289 (1999)
Pauli, H.-C.: Discretized light cone quantization and the effective interaction in hadrons. In: Ji, C.R., Min, D.P. (eds.) New directions in quantum chromodynamics, AIP Conf. Proc. 494 , 80 (1999)
Woloshyn R.M., Jackson A.D.: Comparison of three-dimensional relativistic scattering equations. Nucl. Phys. B 64, 269 (1973)
Sales J.H.O., Frederico T., Carlson B.V., Sauer P.U.: Light-Front Bethe–Salpeter equation. Phys. Rev. C 61, 044003 (2000)
Sales J.H.O., Frederico T., Carlson B.V., Sauer P.U.: Renormalization of the ladder Light-Front Bethe–Salpeter equation in the Yukawa model. Phys. Rev. C 63, 064003 (2001)
Frederico T., Sales J.H.O., Carlson B.V., Sauer P.U.: Light-Front time picture of few-body systems. Nucl. Phys. A 737, 260c (2004)
Diehl M.: Generalized parton distributions. Phys. Rep. 388, 41 (2003)
de Melo J.P.B.C., Frederico T., Pace E., Pisano S., Salmè G.: Time- and spacelike nucleon electromagnetic form factors beyond relativistic constituent quark models. Phys. Lett. B 671, 153 (2009)
Puckett A.J.R. et al.: Recoil polarization measurements of the proton electromagnetic form factor ratio to Q 2 = 8.5 GeV 2. Phys. Rev. Lett. 104, 242301 (2010)
Marinho J.A.O., Frederico T.: Three-Boson systems in Light-Front dynamics. J. Phys. Conf. Series 110, 122009 (2008)
Marinho, J.A.O., Frederico, T.: Next-to-leading order Light-Front three-body dynamics, PoS(LC2008)036
Marinho J.A.O., Frederico T., Sauer P.U.: Light-Front Ward–Takahashi identity and current conservation. Phys. Rev. D 76, 096001 (2007)
Marinho J.A.O., Frederico T., Sauer P.U. (2008) Ward–Takahashi identity for the electromagnetic current of two-particle systems on the light front Few-Body Systems 44: 307
Marinho J.A.O., Frederico T., Pace E., Salmè G., Sauer P.U.: Light-Front Ward–Takahashi identity for two-fermion systems. Phys. Rev. D 77, 116010 (2008)
Gross, F., Stadler, A., Gross, F.: Covariant spectator theory: foundations and applications a mini-review of the covariant spectator theory. Few-Body Syst. (in press)
Karmanov V.A., Mathiot J.-F., Smirnov A.V.: Systematic renormalization scheme in Light-Front dynamics with Fock space truncation. Phys. Rev. D 77, 085028 (2008)
Cooke J.R., Miller G.A.: Ground states of the Wick-Cutkosky (scalar Yukawa) model using Light-Front dynamics, Phys. Rev. C 61, 054008 (2000)
Cooke J.R., Miller G.A., Phillips D.R.: Restoration of rotational invariance of bound states on the light front. Phys. Rev. C 61, 064005 (2000)
Cooke J.R., Miller G.A.: Deuteron binding energies and form factors from Light-Front Hamiltonian field theory, Phys. Rev. C 66, 034002 (2000)
Karmanov V.A., Carbonell J.: Solving Bethe–Salpeter equation in Minkowski space. Eur. Phys. J. A 27, 1 (2006)
Carbonell J., Karmanov V.A.: Cross-ladder effects in Bethe–Salpeter and Light-Front equations. Eur. Phys. J. A 27, 11 (2006)
Hwang D.S., Karmanov V.A.: Many-body Fock sectors in Wick-Cutkosky model. Nucl. Phys. B 696, 413 (2004)
Karmanov V.A., Hwang D.S.: Higher Fock sectors in Wick-Cutkosky model. Few-Body Syst. 36, 155 (2005)
Glazek S.D., Harindranath A., Pinsky S.S., Shigemitsu J., Wilson K.G.: On the relativistic bound state problem in the light front Yukawa model. Phys. Rev. D 47, 1599 (1993)
Mangin-Brinet M., Carbonell J., Karmanov V.A.: Relativistic bound states in Yukawa model. Phys. Rev. D 64, 125005 (2001)
Mangin-Brinet M., Carbonell J., Karmanov V.A.: Two fermion relativistic bound states in light front dynamics. Phys.Rev. C 68, 055203 (2003)
Bakker B.L.G., Boorsma J.K., Ji C.-R.: The box diagram in Yukawa theory. Phys. Rev. D 75, 065010 (2007)
Frederico T.: Null plane model of three bosons with zero range interaction. Phys. Lett. B 282, 409 (1992)
Carbonell J., Karmanov V.A.: Three-boson relativistic bound states with zero-range two-body interaction. Phys. Rev. C 67, 037001 (2003)
de Araújo W.R.B., de Melo J.P.B.C., Frederico T.: Faddeev null plane model of the nucleon. Phys. Rev. C 52, 2733 (1995)
Suisso E.F., de Melo J.P.B.C., Frederico T.: Relativistic dynamics of Qqq systems. Phys. Rev. D 65, 094009 (2002)
Karmanov V.A., Maris P.: Manifestation of three-body forces in three-body Bethe–Salpeter and Light-Front equations. Few Body Syst. 46, 95 (2009)
Gross F., Riska D.O.: Current conservation and interaction currents in relativistic meson theories. Phys. Rev. C 36, 1928 (1987)
Mandelstam S.: Dynamical variables in the Bethe–Salpeter formalism. Proc. Royal Soc. (London) A 233, 248 (1956)
Kvinikhidze A.N., Blankleider B.: Gauge invariant reduction to the light front. Phys. Rev. D 68, 025021 (2003)
de Melo J.P.B.C., Frederico T., Pace E., Salmè G.: Pair term in the electromagnetic current within the front form dynamics: Spin-0 case. Nucl. Phys. A 707, 399 (2002)
Frederico T., Pace E., Pasquini B., Salmè G.: Pion generalized parton distributions with covariant and Light-Front constituent quark models. Phys. Rev. D 80, 054021 (2009)
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Intl. Workshop on Relativistic Description of Two- and Three-body Systems in Nuclear Physics, ECT*, Trento, October 19–23, 2009.
CNPq and FAPESP grants are acknowledged.
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Frederico, T., Salmè, G. Projecting the Bethe–Salpeter Equation onto the Light-Front and Back: A Short Review. Few-Body Syst 49, 163–175 (2011). https://doi.org/10.1007/s00601-010-0163-z
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DOI: https://doi.org/10.1007/s00601-010-0163-z