Reijiro Fukuda

Schwinger-Dyson equation for massless vector theory and the absence of a fermion pole

Abstract The Schwinger-Dyson equation of the fermion propagator in the massless vector theory is discussed. It is found that the Baker-Johnson-Willey solution in lowest approximation is in fact a confining solution: the Fermion propagator has no pole or cut in the time-like region. Discussions of homogeneous and inhomogeneous equations with momentum integration cut-off are also given in some detail.

The Form of Effective Potential

The form of effective potential V with full quantum correction is discussed. Numerical integration using Wilsons recursion formula suggests the convexity of V. The O(N) model with N~co is also discussed with the result that if we suitably regularize the theory renormalized V is convex. The analytic structure of V and W (generating function of connected Greens functions) is studied and mechanism that causes phase transition is discussed.

Gluon Condensation and the Field Strength Formulation in Quantum Chromodynamics

An observation is given that the field strength or the dual potential becomes a good coordinate in the low energy region and that its correlation is of short range if gluons condense in the vacuum in the form of color singlet. Taking the axial gauge the field strength formulation of Quantum Chromodynamics is given after separating the zero mode of the vector potential in order to take into account of the effect of the condensation. It turns out that unstable modes which are present in the spectrum of the vector potential are eliminated by the dual transformation and that the gluonic condensation gives a mass gap to the dual potential. As a dual Meissner effect the flux tube of the color electric field is formed. Numerical estimates of the string tension are given with a value of correct order of magnitude. The same mechanism gives a solution to the U(l) problem. The gluon condensation is finally shown by developing the leading logarithm series of the effective potential which enables us to find the minimum successively for small coupling constant.

Sidewise dispersion calculations for lepton magnetic moment in renormalizable weak interaction models

Abstract We present here the sidewise dispersion calculations for the lepton magnetic moment in Weinbergs type of weak interaction model, in the U-gauge formalism. Unsubtracted sidewise dispersion relations hold, but as for the W and Z boson contributions, our results are different from those obtained by the ξ-limiting procedure. The differences are attributed to the non-commutativity of the dispersion intergration and the ξ →0 limit.