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Connection between the electron propagator and the Baker-Johnson function in conformal invariant quantum electrodynamics

Свяэь между злектронным пропагатором и функцией Бакера-Джонсона в конформной инвариантной квантовой злектродинамике

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Il Nuovo Cimento A (1965-1970)

Summary

The single-electron-line electron propagator of massless quantum electrodynamics is shown to be determined by the product of the Baker-Johnson functionF 1 and the sumE 1 +E 2 of coefficients appearing in the first two terms of theC=−1,J=1 part of the Wilson expansion of the productψ(x)\(\bar \psi \)(y) of electron fields. This statement is subject to the restriction thatE 1 andE 2 are calculated in a special gauge in which massless quantum electrodynamics without electron creation and annihilation is conformal invariant. The possibility of determining the analyticity properties in the coupling constant of the product (E 1+E 2)F 1 from the propagator for an electron in a path-dependent field is discussed.

Riassunto

Si mostra che il propagatore elettronico della linea di un solo elettrone dell’elettrodinamica quantistica in assenza di masse è determinato dal prodotto della funzioneF 1 di Barker-Johnson per la sommaE 1 +E 2 dei coefficienti che compaiono nei primi due termini della parte conC=−1 eJ=1 dello sviluppo di Wilson del prodotto ψ(x)\(\bar \psi \)(y) di campi elettronici. Questa affermazione è soggetta alla restrizione cheE 1 eE 2 siano calcolati in una gauge speciale in cui l’elettrodinamica quantistica in assenza di masse senza creazione e annichilazione di elettroni è conformemente invariante. Si discute la possibilità di determinare le proprietà di analiticità nella costante di accoppiamento del prodotto (E 1 +E 2)F 1 dal propagatore di un elettrone in un campo dipendente dal percorso.

Реэюме

Покаэывается, что злектронный пропагатор в квантовой злектродинамике определяется в виде проиэведения функцииF 1 Бакера-Джонсона и суммы (E 1 +E 2) козффициентов, появляюшихся в первых двух членах для частиC=−1,J=1 раэложения Вильсона проиэведенияψ(x)\(\bar \psi \)(y) злектронных полей. Это утверждение справедливо при условии, чтоE 1 иE 2 вычисляются в специальной калибровке, в которой квантовая злектродинамика беэ рождения и уничтожения злектронов является конформно инвариантной. Обсуждается воэможность определения свойств аналитичности проиэведения (E 1 +E 2)F 1 по констамте свяэи, исходя иэ пропагатора злектрона в поле.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Tübingen, Tübingen

    M. P. Fry

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Supported in part by « Fonds zur Förderung der wissenschaftlichen Forschung in Österreich », project No. 1905 and by the Alexander von Humboldt-Stiftung.

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Fry, M.P. Connection between the electron propagator and the Baker-Johnson function in conformal invariant quantum electrodynamics. Nuov Cim A 31, 129–150 (1976). https://doi.org/10.1007/BF02729928

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