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On quantum field theory — I: explicit solution of Dyson’s equation in electrodynamics without use of feynman graphs

Summary

A compact, explicit expression is given for the term of arbitrary order in the power series expansion of Dyson’sS-matrix, for any arbitrary scattering process. The expression thus found forS has a very high degree of symmetry (a fact which the Feynman graph technique could not reveal; our procedure is also free from several shortcomings of this technique), which suggests the existence in the theory of deeper properties. These will be studied in the continuation to this work.

Riassunto

Si dà una espressione compatta per il termine generico dello sviluppo perturbativo della matriceS di Dyson, per il processo di scattering più generale. Tale sviluppo possiede un alto grado di simmetria, del tutto nascosto dalla tecnica usuale basata sull’uso dei diagrammi di Feynman, che presenta anche vari inconvenienti da cui il nostrometodo è esente. L’espressione trovata perS indica l’esistenza, nella teoria, di più riposte proprietà; queste saranno studiate nel seguito a questo lavoro.

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References

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    F. J. Dyson:Phys. Rev.,75, 486, 1736 (1949).

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    G. C. Wick:Phys. Rev.,80, 268 (1950).

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    E. R. Caianiello andS. Fubini:Nturvo Cimento,9, 1218 (1952) referred to in the text as A.

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    D. Littlewood:The Theory of Group Characters (Oxford, 1950).

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Correspondence to E. R. Caianiello.

Additional information

This work has been in part performed at the Institut for Theoretisk Fysik, Copenhagen, CERN (European Council for Nuclear Eesearch).

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Caianiello, E.R. On quantum field theory — I: explicit solution of Dyson’s equation in electrodynamics without use of feynman graphs. Nuovo Cim 10, 1634–1652 (1953). https://doi.org/10.1007/BF02781659

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