Equivalence of renormalized covariant and light-front perturbation theory: I. Longitudinal divergences in the Yukawa model

Light-front perturbation theory has been proposed as an alternative to covariant perturbation theory. Light-front perturbation theory is only acceptable if it produces invariant S-matrix elements. Doubts have been raised concerning the equivalence of light-front and covariant perturbation theory. One of the obstacles to a rigorous proof of equivalence is the occurrence of longitudinal divergences not present in covariant perturbation theory. We show in the case of the Yukawa model of fermions interacting with scalar bosons at the one-loop level how to deal with the longitudinal divergences. Invariant S-matrix elements are obtained using our method.Comment: 11 pages, epsf, revtex, contains more elaborate explanation of Forced Instantaneous Loops (FILs

The Vector Meson Form Factor Analysis in Light-Front Dynamics

We study the form factors of vector mesons using a covariant fermion field theory model in $(3+1)$ dimensions. Performing a light-front calculation in the $q^+ =0$ frame in parallel with a manifestly covariant calculation, we note the existence of a nonvanishing zero-mode contribution to the light-front current $J^+$ and find a way of avoiding the zero-mode in the form factor calculations. Upon choosing the light-front gauge (\ep^+_{h=\pm}=0) with circular polarization and with spin projection $h=\uparrow\downarrow=\pm$, only the helicity zero to zero matrix element of the plus current receives zero-mode contributions. Therefore, one can obtain the exact light-front solution of the form factors using only the valence contribution if only the helicity components, $(h'h)=(++),(+-)$, and $(+0)$, are used. We also compare our results obtained from the light-front gauge in the light-front helicity basis (i.e. $h=\pm,0$) with those obtained from the non-LF gauge in the instant form linear polarization basis (i.e. $h=x,y,z$) where the zero-mode contributions to the form factors are unavoidable.Comment: 33 pages; typo in Eq.(15) is corrected; comment on Ref.[9] is corrected; version to appear in Phys. Rev.

Compactification near and on the light front

We address problems associated with compactification near and on the light front. In perturbative scalar field theory we illustrate and clarify the relationships among three approaches: (1) quantization on a space-like surface close to a light front; (2) infinite momentum frame calculations; and (3) quantization on the light front. Our examples emphasize the difference between zero modes in space-like quantization and those in light front quantization. In particular, in perturbative calculations of scalar field theory using discretized light cone quantization there are well-known ``zero-mode induced'' interaction terms. However, we show that they decouple in the continuum limit and covariant answers are reproduced. Thus compactification of a light-like surface is feasible and defines a consistent field theory.Comment: 24 pages, 4 figure

Relativistic bound states in Yukawa model

The bound state solutions of two fermions interacting by a scalar exchange are obtained in the framework of the explicitly covariant light-front dynamics. The stability with respect to cutoff of the J$^{\pi}$=$0^+$ and J$^{\pi}$=$1^+$ states is studied. The solutions for J$^{\pi}$=$0^+$ are found to be stable for coupling constants $\alpha={g^2\over4\pi}$ below the critical value $\alpha_c\approx 3.72$ and unstable above it. The asymptotic behavior of the wave functions is found to follow a ${1\over k^{2+\beta}}$ law. The coefficient $\beta$ and the critical coupling constant $\alpha_c$ are calculated from an eigenvalue equation. The binding energies for the J$^{\pi}$=$1^+$ solutions diverge logarithmically with the cutoff for any value of the coupling constant. For a wide range of cutoff, the states with different angular momentum projections are weakly split.Comment: 22 pages, 13 figures, .tar.gz fil

Infinite Nuclear Matter on the Light Front: Nucleon-Nucleon Correlations

A relativistic light front formulation of nuclear dynamics is developed and applied to treating infinite nuclear matter in a method which includes the correlations of pairs of nucleons: this is light front Brueckner theory. We start with a hadronic meson-baryon Lagrangian that is consistent with chiral symmetry. This is used to obtain a light front version of a one-boson-exchange nucleon-nucleon potential (OBEP). The accuracy of our description of the nucleon-nucleon (NN) data is good, and similar to that of other relativistic OBEP models. We derive, within the light front formalism, the Hartree-Fock and Brueckner Hartree-Fock equations. Applying our light front OBEP, the nuclear matter saturation properties are reasonably well reproduced. We obtain a value of the compressibility, 180 MeV, that is smaller than that of alternative relativistic approaches to nuclear matter in which the compressibility usually comes out too large. Because the derivation starts from a meson-baryon Lagrangian, we are able to show that replacing the meson degrees of freedom by a NN interaction is a consistent approximation, and the formalism allows one to calculate corrections to this approximation in a well-organized manner. The simplicity of the vacuum in our light front approach is an important feature in allowing the derivations to proceed. The mesonic Fock space components of the nuclear wave function are obtained also, and aspects of the meson and nucleon plus-momentum distribution functions are computed. We find that there are about 0.05 excess pions per nucleon.Comment: 39 pages, RevTex, two figure

Light-Front Bethe-Salpeter Equation

A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests that the convergence of the expansion is rapid. This result is particular for light-front dynamics. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional ones. The technical procedure is developed for a two-boson case; the idea for an extension to fermions is given. The technical procedure appears quite practicable, possibly allowing one to go beyond the ladder approximation for the solution of the Bethe-Salpeter equation. The relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter equation and a corresponding quantum-mechanical description is discussed.Comment: 42 pages, 5 figure

Electromagnetic form factors in the light-front formalism and the Feynman triangle diagram: spin-0 and spin-1 two-fermion systems

The connection between the Feynman triangle diagram and the light-front formalism for spin-0 and spin-1 two-fermion systems is analyzed. It is shown that in the limit q+ = 0 the form factors for both spin-0 and spin-1 systems can be uniquely determined using only the good amplitudes, which are not affected by spurious effects related to the loss of rotational covariance present in the light-front formalism. At the same time, the unique feature of the suppression of the pair creation process is maintained. Therefore, a physically meaningful one-body approximation, in which all the constituents are on their mass-shells, can be consistently formulated in the limit q+ = 0. Moreover, it is shown that the effects of the contact term arising from the instantaneous propagation of the active constituent can be canceled out from the triangle diagram by means of an appropriate choice of the off-shell behavior of the bound state vertexes; this implies that in case of good amplitudes the Feynman triangle diagram and the one-body light-front result match exactly. The application of our covariant light-front approach to the evaluation of the rho-meson elastic form factors is presented.Comment: corrected typos in the reference