On quantum field theory. II: Non-perturbative equations and methods View Full Text


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Article Info

DATE

1954-05

AUTHORS

E. R. Caianiello

ABSTRACT

The evaluation of an element of theU-matrix between arbitrary initial and final states is reduced to that of a kernel, whose form depends only upon the number of particles involved and is given explicity as a perturbative expansion. Kernels are shown to satisfy systems of «branching equations», which hold independently of perturbation methods and can be taken as the axiomatic foundation of the theory, Lorentz covariance being manifest. Complete systems of such equations are given for the kernels and their derivatives with respect to the interaction strength λ: all other conceivable equations among kernels are necessarily deducible from them. All kernels corresponding to processes involving real bosons can be obtained, with simple integrations, from the kernels for purely fermionic processes; the branching equations for these are also explicity given and suffice to define the theory. A kernel, with its first and second λ-derivatives, satisfies a single integral relation. A variety of approximation methods are immediately deducible from the branching equations; they, while extending and generalizing the known ones, always permit, at least in principle, tests of convergence. Questions of renormalization, existence of solutions, etc., will be studied in the sequel to this paper. More... »

PAGES

492-529

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02781043

DOI

http://dx.doi.org/10.1007/bf02781043

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1006501346


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