Summary
A natural way to determine the renormalization constants of the nonlinear σ-model with only one extra parameter is presented; PCAC relations are fulfilled at all orders. This method is explicitly developed for one-loop graphs involving nucleons.
Riassunto
Si presenta un metodo naturale per determinare le costanti di rinormalizzazione del modello σ non lineare con un solo parametro addizionale; le relazioni di PCAC sono soddisfatte in tutti gli ordini. Si sviluppa esplicitamente il metodo sui grafici ad una ansa che coinvolgono nucleoni.
Реэюме
Предлагается естественный путь определения перенормировочных постоянных нелинейнойс-модели с единственным дополнительным параметром. Соотнощения PCAC выполняются во всех порядках. Этот метод в явном виде рассматривается на графиках с одной петлей, включаюших нуклоны.
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References
M. Gell-Mann:Phys. Rev.,125, 1067 (1962);Physics,1, 63 (1964). See also a review paper on chiral symmetry:S. Gasiorowicz andD. A. Geffen:Rev. Mod. Phys.,41, 531 (1969).
References on practical calculations can be found in the review paper ofJ. Zinn-Justin:Phys. Reports,1 C, 3 (1971).
M. Gell-Mann andM. Levy:Nuovo Cimento,16, 705 (1960).
B. W. Lee:Nucl. Phys.,9 B, 649 (1969).
J. L. Gervais andB. W. Lee:Nucl. Phys.,12 B, 627 (1969).
K. Symanzik:Comm. Math. Phys.,16, 48 (1970);Lett. Nuovo Cimento,16, 705 (1970).
J. A. Mignaco andE. Remiddi:Nuovo Cimento,1 A, 395 (1971).
Calculations about the NLM, to be published: ππR. Barlow, πN M. C. Bergere andJ. M. Drouffe, N N D. Bessis, G. Turchetti andW. Wortman.
R. Barlow andM. C. Bergere:Nucleon-nucleon scattering lengths and Padé approximants, Saclay preprint DPhT/71–72.
S. Weinberg:Phys. Rev. Lett.,18, 188 (1967);W. A. Bardeen andB. W. Lee:Phys. Rev.,177, 2389 (1969).
R. Barbieri andE. Remiddi:Lett. Nuovo Cimento,4, 466 (1970).
D. Bessis andJ. Zinn-Justin:Phys. Rev. D,5, 1313 (1972).
D. Bessis andG. Turchetti:Cargèse Summer School, 1970.
D. Bessis andG. Turchetti: private communication.
M. C. Bergere andJ. M. Drouffe: in preparation.
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Attaché de recherche au CNRS.
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Bergere, M.C., Drouffe, J.M. A possible renormalization of the nonlinearσ-model. Nuov Cim A 11, 121–138 (1972). https://doi.org/10.1007/BF02722782
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DOI: https://doi.org/10.1007/BF02722782