No abstract

A recently proposed perturbative technique for quantum field theory consists of replacing nonlinear terms in the Lagrangian such as φ4 by (φ2)1+δ and then treating δ as a small parameter. It is shown here that the same approach gives excellent results when applied to difficult nonlinear differential equations such as the Lane–Emden, Thomas–Fermi, Blasius, and Duffing equations.

It has been recognized for some time that quantization on a null plane has several unique and remarkable advantages for the elucidation of quantum field theories. To date these unique features have not been exploited to solve strongly coupled, four-dimensional gauge theories. This is the first in a series of papers aimed at systematically formulating renormalizable gauge theories on the null plane. In order to lay down the groundwork for upcoming nonperturbative studies, it is indispensable to gain control over the perturbative treatment first. A discussion of one-loop renormalization of QED in the Hamiltonian formalism is presented. In this approach, one is faced with severe infrared divergences characteristic of the light-cone gauge. We show how to treat these divergences in a coherent fashion, and thus recover the usual results of the renormalization procedure such as Ward identities and coupling-constant renormalizations.

We study spontaneous symmetry breaking in (l+l)-dimensional qh4 theory using the light-front formulation of field theory. Since the physical vacuum is always the same as the perturbative vacuum in light-front field theory the fields must develop a vacuum expectation value through the zero-mode components of the field. We solve the nonlinear operator equation for the zero mode in the one-mode approximation. We find that spontaneous symmetry breaking occurs at Xcritical = 47r (3 + 4 p 2 , which is consistent with the value Xc,itic,l = 54.27p2 obtained in the equal-time theory. We calculate the vacuum expectation value as a function of the coupling constant in the broken phase both numerically and analytically using the 6 expansion. We find two equivalent broken phases. Finally we show that the energy levels of the system have the expected behavior for the broken phase. PACS number(s): ll.lO.Ef, 11.30.Q~

We consider the (1ϩ1)-dimensional Nϭ(8,8) supersymmetric matrix field theory obtained from a dimensional reduction of ten dimensional Nϭ1 super Yang-Mills theory. The gauge groups we consider are U(N) and SU(N), where N is finite but arbitrary. We adopt light-cone coordinates, and choose to work in the light-cone gauge. Quantizing this theory via discretized light-cone quantization ͑DLCQ͒ introduces an integer, K, which restricts the light-cone momentum-fraction of constituent quanta to be integer multiples of 1/K. Solutions to the DLCQ bound state equations are obtained for Kϭ2, 3 and 4 by discretizing the light-cone super charges, which preserves supersymmetry manifestly. We discuss degeneracies in the massive spectrum that appear to be independent of the light-cone compactification, and are therefore expected to be present in the decompactified limit K→ϱ. Our numerical results also support the claim that the SU(N) theory has a mass gap. ͓S0556-2821͑98͒01922-5͔