On the light-cone quantization of non-abelian gauge theory

The implications of periodic boundary conditions in the light-cone quantization of non-abelian fields are studied. Formulation of the theory in the singularity-free case is presented. Some consequences of field singularities are discussed.     

On the light-cone formulation of classical non-abelian gauge theory

For a classical Yang-Mills field which is periodic in the longitudinal light-cone coordinate: (a) a gauge condition is formulated, (b) the presence of field singularities in this gauge is shown, and (c) the relevance of these singularities to the topological charge is demonstrated.Also of the Science Sector, UNESCO     

On zero modes and gauge fixing in light-cone quantized gauge theories

It is shown that regularistation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.

     

QCD calculations in the light-cone gauge

The non-singlet quark structure function is calculated in the leading logarithm approximation in an axial gauge with n² = 0, the light-cone gauge. The choice n² = 0 leads to a simple identity for loop integrals involving the extra n · k denominators. We compare the results graph by graph with both Feynman gauge QCD and a scalar gluon theory. The leading diagrams are the same “rainbow” diagrams as for the case of the scalar theory.The techniques are also applied to quark-quark scattering at large transverse momentum. The leading diagrams have the same dressed ladder-form factor structure.     

One-loopN-point functions in the light-cone gauge

We consider, in the light-cone gauge, the possible structure of the counterterms arising in the solution to the renormalization equation. Using the structure of these counterterms and the noncovariant formalism of the integrals as guidelines, we also examine to one-loop order the divergence and nonlocality of theN-point gluon vertex functions forN≧5.     

Multi-loops for light-cone gauge superstrings

After closure of the [10]-SUSY algebra, the full light-cone gauge field theory of superstrings is reduced to a set of general integral representations of first quantised form for multi-loop diagrams. These are then reduced further, by a limiting procedure, to an explicitly Lorentz-covariant expression for these diagrams. No summations over spin structures or odd supermoduli are required. The low energy cosmological constant and all N = 2 and 3amplitudesare zero at all loop orders.     

The Nappi-Witten string in the light-cone gauge

Some of the motivations for as well as the main points of the quantization of the Nappi-Witten string in the light-cone gauge are reviewed.     

Interacting membrane picture in the light-cone gauge

An attempt is made to formulate the interacting membrane picture in the light-cone gauge, which is analogous to the interacting string picture of Mandelstam. The possible emission of strings from the membrane is also discussed.     

The triangle anomaly in the light-cone gauge

It is shown that the triangle anomaly can be evaluated in the light-cone gauge and that the result obtained is consistent with the usual covariant one. We use two different procedures: (i) Eliminating the nonphysical fields from the covariant anomalous Ward identity. (ii) Carrying out a chiral transformation on the light-cone Lagrangian. The use of both dimensional and Pauli-Villars regularisations are discussed.     

The exceptional Jordan algebra and the superstring

Two representations of the exceptional Jordan algebra are presented, one in terms of bose vertex operators, and the other in terms of superstring vertex operators in bosonised form, including their BRST ghost contributions. It is also shown how the non-exceptional Jordan algebras may be constructed similarly.     

Melosh transformation and light-cone current algebra

An investigation is made of the consequences of combining light-cone current algebra with the Melosh transformation as applied to nucleonic matrix elements of local currents and of the local limits of derivatives of bilocal currents. These lead to various sum-rule equalities and inequalities for the deep inelastic scale functions, both unpolarized and polarized.     

Renormalization of Wilson operators in the light-cone gauge

We test the renormalization of Wilson operators and the Mandelstam–Leibbrandt gauge in the case when the sides of the loop are parallel to the vectors used in the M–L gauge. Graphs which in the Feynman gauge are free of ultra-violet divergences, in the M–L gauge show double divergences and single divergences with non-local Si and Ci functions. These non-local functions cancel out when we add all graphs together and the constraints of gauge invariance are satisfied. In Appendix C we briefly discuss the problems of the M–L gauge for loops containing spacelike lines. Received: 31 May 2000 / Published online: 23 January 2001     

Cut-off versus dimensional regularization in the light-cone gauge

The conventional cut-off method is applied to massless light-cone gauge Feynman integrals. Despite the presence of non-local terms in the unintegrated expression for the Yang-Mills self-energy, the cut-off procedure yields the same ultra-violet behaviour as the lengthier technique of dimensional regularization.     

Analysis of weak neutral currents using light-cone algebra

Using the algebra of light-cone commutators and making some simplifying assumptions, we have attempted to determine the isospin structure of a two-parameter weak hadronic neutral current. We have also computed in the light-cone model, they distributions for inclusive neutrino and antineutrino neutral current deep-inelastic interactions. Contrary to the quark-parton model, we find that both distributions have the same value.     

Ghost-free formulation of quantum gravity in the light-cone gauge

By choosing the light-cone gauge, we remove all redundant components of the metric tensor as well as all Faddeev-Popov ghosts from the Einstein Lagrangian, from which Feynman rules for two independent transverse components can be immediately formulated. The 2 + 2 decomposition of the metric tensor proves to be simpler than the usual canonical 1 + 3 decomposition, so that all spurious components can be explicitly eliminated from the spectrum. Because the Lagrangian is now only a function of independent components, it is possible to study the unresolved problem of the functional measure for quantum gravity. We are presently studying the measure problem.