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• W2019677911 endingPage "B829" @default.
• W2019677911 startingPage "B816" @default.
• W2019677911 abstract "The principal objective of the present work is the derivation of conditions for equivalence (A) between a four-Fermi theory with pseudoscalar coupling and a Yukawa theory with pseudoscalar bosons, and (B) in the corresponding vector case. In general, two conditions are found to be both necessary and sufficient. The first is a condition for the existence of an appropriate boson bound state in the four-Fermi theory. The second condition is that the boson wave function renormalization constant ${Z}_{3}$ in the Yukawa theory be equal to zero. We first derive our results by consideration of fermion-fermion scattering in the chain approximation, and proceed afterwards to prove them valid to all orders in perturbation theory. We also discuss the degenerate vacuum theories of Nambu and Jona-Lasinio and of Bjorken in the chain approximation. In each of these four-Fermi theories, the existence of boson bound states (massless pseudoscalar and massive scalar bosons in the former case, massless vector bosons in the latter) follows automatically from self-consistency conditions. Hence to have equivalence to Yukawa theories in which the bosons are described by elementary fields, we need only impose the ${Z}_{3}=0$ conditions on the Yukawa theories. Finally, we comment on Birula's theory of quantum electrodynamics without electromagnetic field. It is to be stressed that we deal throughout with full-scale relativistic field theories of physical consequence." @default.
• W2019677911 created "2016-06-24" @default.
• W2019677911 creator A5006452618 @default.
• W2019677911 creator A5072378013 @default.
• W2019677911 date "1964-11-09" @default.
• W2019677911 modified "2023-09-24" @default.
• W2019677911 title "Equivalence Between Four-Fermion and Yukawa Coupling, and the<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msub><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mn /></mml:math>Condition for Composite Bosons" @default.
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• W2019677911 doi "https://doi.org/10.1103/physrev.136.b816" @default.
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