Light-front Perturbation Theory Research Articles

Comparison of quantum field perturbation theory for the light front with the theory in Lorentz coordinates

The relationship between the perturbation theory in light-front coordinates and Lorentz-covariant perturbation theory is investigated. A method for finding the difference between separate terms of the corresponding series without their explicit evaluation is proposed. A procedure of constructing additional counter-terms to the canonical Hamiltonian that compensate this difference at any finite order is proposed. For the Yukawa model, the light-front Hamiltonian with all of these counter-terms is obtained in a closed form. Possible application of this approach to gauge theories is discussed.

Angular momentum and light-front scattering theory.

The role of the Leutwyler and Stern spin operator in the angular momentum analysis of light-front scattering theory is analyzed. The equations of formal scattering theory are transformed to the $\ensuremath{\xi}$ picture using the unitary operator $C(\ensuremath{\xi})$ recently developed by the author. This operator depends on the two angles which determine the direction of the three-vector part of a lightlike four-vector $\ensuremath{\xi}$. It is shown that an invariant version of light-front perturbation theory developed earlier by the author is related to the standard theory by the unitary operator $C(\ensuremath{\xi})$. It is also shown how to carry out a partial-wave analysis of the Lippmann-Schwinger-like equations obtained by summing a subset of the diagrams of this invariant form of light-front perturbation theory. The analysis presented here makes clear that the $\ensuremath{\xi}$ picture overcomes many of the difficulties due to the interaction dependence of light-front angular momentum operators, in particular the difficulties arising from the fact that the individual diagrams of light-front pertubation theory are not rotationally invariant.

Erratum: Lowest-order mass corrections for a (1+1)-dimensional Yukawa model in light-front perturbation theory

In this work we {ital explicitly} demonstrate the equivalence of covariant (Feynman) perturbation theory with noncovariant light-front perturbation theory (LFPT) for lowest-order self-energy corrections in the (1+1)-dimensional Yukawa model. We also perform calculations in old-fashioned perturbation theory in the infinite-momentum frame (OFPT{sub {infinity}}) to elucidate the differences between LFPT and OFPT{sub {infinity}}.

Lowest-order mass corrections for a (1+1)-dimensional Yukawa model in light-front perturbation theory.

In this work we explicitly demonstrate the equivalence of covariant (Feynman) perturbation theory with noncovariant light-front perturbation theory (LEPT) for lowest-order self-energy corrections in the (1+1)-dimensional Yukawa model. We also perform calculations in oldfashioned perturbation theory in the infinite-momentum frame ($\mathrm{OFP}{\mathrm{T}}_{\ensuremath{\infty}}$) to elucidate the differences between LFPT and $\mathrm{OFP}{\mathrm{T}}_{\ensuremath{\infty}}$.

Invariant light front perturbation theory.

It is shown that with the introduction of an external lightlike vector, a light front perturbation theory for the S matrix in quantum field theory can be developed in which the individual terms in the series are invariant functions of the particle variables and the external vector. No limiting processes are involved. The dependence of the results on the external lightlike vector is discussed.

Covariant light front perturbation theory and three-particle equations.

A covariant version of light front perturbation theory is obtained as a limit of the covariant time-ordered perturbation theory developed recently by the author. The graphical rules for the covariant light front perturbation theory are essentially the same as Weinberg's infinite momentum frame rules; however, they involve a redefinition of the original Weinberg variables. The new definitions guarantee that the contributions of individual diagrams to the S matrix are invariant. A set of manifestly invariant three-particle integral equations is derived. These equations are obtained from a model field theory which describes the interaction of a charged scalar particle \ensuremath{\psi} with a neutral scalar particle \ensuremath{\varphi} according to the virtual process \ensuremath{\psi}\ensuremath{\rightleftarrows}\ensuremath{\psi}+\ensuremath{\varphi}. The solutions of the integral equations lead to amplitudes for \ensuremath{\varphi}+\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\varphi}+\ensuremath{\psi} and \ensuremath{\varphi}+\ensuremath{\psi}\ensuremath{\rightarrow}2\ensuremath{\varphi}+\ensuremath{\psi} which satisfy two- and three-particle unitarity. The integral equations are free of the spurious singularity in s, the square of the invariant c.m. energy, which has been an undesirable feature of earlier relativistic three-particle equations. This singularity is known to be responsible for spurious bound state solutions.