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In this paper the question of the asymptotic conformal invariance of the off-shell amplitude for the process π0→ 2 γ has been investigated. It has been shown that the off-shell amplitude for the process concerned can be given an asymptotically conformal covariant form by using a parton model description of the neutral pion instead of treating the pion as an elementary particle. This investigation shows that the conclusion regarding the question of the asymptotic conformal invariance of the off-shell amplitude for the process π0→ 2 γ obtained from the parton model along with the use of conformal covariant operator product expansions is the same as that of the Johnson-Baker-Willey version of finite QED from which the asymptotic conformal invariance of the 3-point Green's function for the process π0→ 2 γ follows as a necessary consequence.

In a previous paper, we considered a perturbation solution for propagation of the fourth-order coherence function in a random medium. In this paper, it is shown how under certain conditions this solution may be extended to treat the propagation problem when the field fluctuations need not be small. A differential equation governing the fourth-order coherence function is derived. A solution is obtained in the geometric-optics limit when the four points of the coherence function are distinct.

In many semiconductors and insulators electronic absorption occurs below the direct electron-energy gap, owing (we assume) to the interaction of electrons with optical phonons. In this paper we compare absorption coefficients, over a wide range of interaction strengths, calculated by two different prescriptions. The first method is a perturbative one, which takes into account only one-phonon processes, while the second is a nonperturbative method, which takes into account many-phonon processes.We find that for the (weak) interaction involved in InSb the two methods give essentially the same results for photon energies in the interval [Eg– kθ, Eg], where Egis the energy gap and kθ is the optical phonon energy. For stronger interactions the perturbation results are nowhere applicable.