Quantum Electrodynamics at Large Distances III: Verification of Pole Factorization and the Correspondence Principle

In two companion papers it was shown how to separate out from a scattering function in quantum electrodynamics a distinguished part that meets the correspondence-principle and pole-factorization requirements. The integrals that define the terms of the remainder are here shown to have singularities on the pertinent Landau singularity surface that are weaker than those of the distinguished part. These remainder terms therefore vanish, relative to the distinguished term, in the appropriate macroscopic limits. This shows, in each order of the perturbative expansion, that quantum electrodynamics does indeed satisfy the pole-factorization and correspondence-principle requirements in the case treated here. It also demonstrates the efficacy of the computational techniques developed here to calculate the consequences of the principles of quantum electrodynamics in the macroscopic and mesoscopic regimes.Comment: latex, 39 pages, 2 Figures included as uuencoded, tarred, gzipped, encapsulated postscript files, uses math_macros.te

T-duality of ZZ-brane

We examine how nonperturbative effects in string theory are transformed under the T-duality in its nonperturbative framework by analyzing the c=1/2 noncritical string theory as a simplest example. We show that in the T-dual theory they also take the form of exp(-S_0/g_s) in the leading order and that the instanton actions S_0 of the dual ZZ-branes are exactly the same as those in the original c=1/2 string theory. Furthermore we present formulas for coefficients of exp(-S_0/g_s) in the dual theory.Comment: 37 pages, no figure, LaTeX; (v2) version published in Physical Review

Asymmetric Non-Abelian Orbifolds and Model Building

The rules for the free fermionic string model construction are extended to include general non-abelian orbifold constructions that go beyond the real fermionic approach. This generalization is also applied to the asymmetric orbifold rules recently introduced. These non-abelian orbifold rules are quite easy to use. Examples are given to illustrate their applications.Comment: 30 pages, Revtex 3.

Scaling Behavior of Ricci Curvature at Short Distance near Two Dimensions

We study the renormalization of the Ricci curvature as an example of generally covariant operators in quantum gravity near two dimensions. We find that it scales with a definite scaling dimension at short distance. The Ricci curvature singularity at the big bang can be viewed as such a scaling phenomenon. The problem of the spacetime singularity may be resolved by the scale invariance of the spacetime at short distance.Comment: 9pages, LaTe

Quantum Electrodynamics at Large Distances II: Nature of the Dominant Singularities

Accurate calculations of macroscopic and mesoscopic properties in quantum electrodynamics require careful treatment of infrared divergences: standard treatments introduce spurious large-distances effects. A method for computing these properties was developed in a companion paper. That method depends upon a result obtained here about the nature of the singularities that produce the dominant large-distance behaviour. If all particles in a quantum field theory have non-zero mass then the Landau-Nakanishi diagrams give strong conditions on the singularities of the scattering functions. These conditions are severely weakened in quantum electrodynamics by effects of points where photon momenta vanish. A new kind of Landau-Nakanishi diagram is developed here. It is geared specifically to the pole-decomposition functions that dominate the macroscopic behaviour in quantum electrodynamics, and leads to strong results for these functions at points where photon momenta vanish.Comment: 40 pages, 11 encapsulated postscript figures, latexed, math_macros.tex can be found on Archive. full postscript available from http://theorl.lbl.gov/www/theorgroup/papers/35972.p