Summary
A variant of the « finite » field theory approach of Gell-Mann and Low is presented in a massless quark model with singlet gluons. A solution is exhibited for which the gluon wave function renormalization constant is finite but with the quark bare mass infinite. Its spacetime structure is very different from the zero-physical-mass limit of the Adler-Baker-Johnson-Willey electrodynamics. The quark propagator exhibits a square-root cut running fromp 2 = 0 to ∞ and it breaksγ 5-invariance but yet preserves scale invariance. The quark-gluon substructure remains unobservable. An interesting consequence of the model is the departure of the e+e− annihilation cross-section into hadrons from the free-quark model result. The other features area) the existence of Goldstone bosons,b) an explicit realization of Kallén’s conjecture in quantum electrodynamics andc) a counter-example to the extension of the Federbush-Johnson-Jost-Schröer theorem outside the charge-zero sector of the present model.
Riassunto
Si presenta una variante dell’approccio della teoria dei campi «finita» di Gell-Mann e Low in un modello di quark senza massa con gluoni di singoletto. Si presenta una soluzione per cui la costante di rinermalizzazione della funzione d’onda del gluone è finita ma con la massa nuda del quark infinita. La sua struttura spazio-temporale è molto diversa dal limite di massa fisica nulla dell’elettrodinamica di Adler-Baker-Johnson-Willey. Il propagatore dei quark presenta un taglio di radice quadrata che va dap 2 = 0 a ∞ e infrange l’invarianza γ5 ma tuttavia conserva l’invarianza di scala. Non si osserva la sottostruttura dei quark-gluoni. Un’interessante conseguenza del modello è la deviazione delle sezioni d’urto di annilazione e+e− in adroni dal risultato del modello di quark liberi. Le altre caratteristiche sonoa) l’esistenza di bosoni di Goldstone,b) una realizzazione esplicita della congettura di Kallén nell’elettrodinamica quantistica ec) un controesempio all’estensione del teorema di Federbush-Johnson-Jost-Schröer al di fuori del settore di carica nulla del presente modello.
Реэюме
Предлагается вариант « конечной » теории поля Гелл-Мана и Лоу в модели кварков с нулевой массой и синглетными глуонами. Приводится рещение, для которого постоянная перенормировки волновой функции глуона является конечной, но с бесконечной массой « голого » кварка. Пространственно-вре менная структура сильно отличается от предела нулевой фиэической массы для злектродинамики Адлера-Бакера-Джонсо на-Виллея. Пропагатор кварка имеет раэреэ типа квадратного корня, который проходит отp 2 = 0 до ∞, при зтом нарущается γ5 инвариантность, но сохраняется масщтабная инвариантность. Кварк-глуонная субструктура остается ненаблюдаемой. Интересное следствие предложенной модели представляет отклонение поперечного сечения e+e− аннигиляции в адроны от реэультата, полученного с помошью модели свободных кварков. Следует отметить другие особенности модели: 1) сушествование боэонов Голдстоуна, 2) явная реалиэация предположения Челлена в квантовой злектродинамике и 3) контр-пример для испольэования теоремы Федербуща-Джонсона-о ста-Щрёера вне сектора с нулевым эарядом для предложенной модели.
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Supported by DFG grant No. K1 256/4.
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Acharya, R., Horváth, Z. Scale invariance and chiral noninvariance in a four-dimensional interacting field theory. Nuov Cim A 33, 47–63 (1976). https://doi.org/10.1007/BF02748684
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DOI: https://doi.org/10.1007/BF02748684