Abstract
Barring lepton electrodynamics, most Lagrangians of physical interest are “non-renormalizable”, the apparent non-renormalizability arising either from their non-polynomial nature or from higher spins.
Presented at the Coral Gables Conference, Miami, January 23–25,1970,and the IX. Internationale Universitätswochen für Kernphysik, Schladming, February 23 — March 7, 1970.
On leave of absence from Imperial College, London,England.
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S. Fells (UCLA preprint) has shown that the vacuum self-energy of 3-like non-polynomial Lagrangians which are
odd in powers of do not possess a
lower bound. Presumably 4 -like even theories do not
suffer from this objection. Our use of a mixed power
theory l/(l+f) is purely to illustrate the necessary
techniques. Physical theories (like the chiral theory) are even in field variables.
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While this was being printed, Dr. 0. V. Steinmann (Zürich) has sent a preprint which shows that, for nonpolynomial theories, the scattering matrix exists in an axiomatic formulation and also that the LSZ reduction procedure can be carried through even though, for rational non-polynomial theories, strict local commutativity may possibly not hold. It appears that the quiet revolution which has been taking place with non-polynomial physics may acquire respectability yet.
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Salam, A. (1970). Non-Polynomial Lagrangian Theories. In: Urban, P. (eds) Developments in High Energy Physics. Acta Physica Austriaca, vol 7/1970. Springer, Vienna. https://doi.org/10.1007/978-3-7091-5835-7_1
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