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We present a simple argument which shows that all the ultraviolet divergences of quantum field theory may be subtracted by the use of purely local Hermitian counterterms. Using minimal subtraction and differentiation with respect to external momenta we are able to circumvent the problem of overlapping divergences, and many results of renormalization theory are easily derived. The subtraction procedure also allows arbitrary infrared well-defined rearrangements of the regularized integrand to be carried out.

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The authors have analyzed the terms of relative order a'1n(a ') that come from annihilation kernels in positronium, and have found a contribution of a ln(a ')m, /24 to -positronium hyperfine splitting from annihilation kernels, including several new contributions. The resulting hyperfine splitting is 203.4003 GHz, with terms of order a m, /2-0. 01 6Hz uncomputed. The contributions to the decay rates of orthoand parapositronium have also been calculated. For orthopositromum the result isn'ln(a ')I 0/3. The authors present in more detail the theoretical analysis leading to their previous nl o calculation and improve on the numerical results. The resulting theoretical orthopositronium decay rate is 7.0386+0;0002 p, sec ', with terms of order a I 0 = 0.0004 p,sec ' uncalculated.

We propose a new relativistic two-body formalism which reduces to a nonrelativistic Schroedinger theory for a single effective particle. The formalism is equal in rigor to that of Bethe and Salpeter, and considerably simpler to apply. We illustrate its use by computing O(or6) terms in the ground state splitting of muonium and positronium involving infinite Coulomb exchange.

The results of a new calculation of the 0(a) corrections to the decay rate of orthopositronium are presented. The rate is r = r°[l-(O/TT) (10.348 ± 0.070)] = (7.0379 ±0.0012) x 10 6 sec" 1 . This is substantially below all measured rates as well as previous theoretical estimates. We provide further justification for the computational techniques employed.The decay rite of orthopositronium into three photons is the only decay rate of a purely quantum electrodynamic system that has been measured to an accuracy of better than 1%. The possibility suggested by recent experiments 1 ' 3 of as much as a 2% discrepancy between existing theory and experiment necessitates a critical re-examination of the theory. In this Letter we present the results of a new calculation of all order-ot correction to this decay rate. The complete problem was first considered by Stroscio and Holt. 3 Although we agree with the method of computation employed by these authors, our final result is considerably lower than their rate. We obtain T 0 -PS-> 3r = r°[l-(a/7r)(10.348± 0.070)] = (7.0379± 0.0012) xltf 5 sec" 1 , where r° is the lowest-order rate: n0 _q 6 m e c 2 2(77 2 • 9) n 9TT