THE SPECTRAL REPRESENTATION OF PROPAGATOR FOR FERMION FIELD AND QUARK CONFINEMENT

GAO CHONG-SHOU; RUAN TU-NAN

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2024年10月30日

Chinese Physics C> 1981, Vol. 5> Issue(3) : 273-281

THE SPECTRAL REPRESENTATION OF PROPAGATOR FOR FERMION FIELD AND QUARK CONFINEMENT

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Abstract：
The properties of fermion causal Green's function is discussed according to the theory of spectral representation. The definition of effective mass is established from the view point of field theory, and the approximate expression of S_F' (p) as |p²|«M² and the asymptotic formula of S_F' (p) as p²→+∞ is given. In terms of these result the problem of quark confinement is discussed. We find that: (ⅰ) Based on the theory of spectral re presentation the concept of relative confinement is allowed, and if renormalization effect is strong, the quarks can demonstrate definitely lighter effective mass when they are far away from the mass shell; (ⅱ) Based on the theory of spectral representation the concept of absolute confinement is unallowable, even the absolute confinement is taken as the limit of relative confinement. That is if the concept of absolute confinement is introduced, we must discard a part of elementary hypothesis of spectral representation theory.

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GAO CHONG-SHOU and RUAN TU-NAN. THE SPECTRAL REPRESENTATION OF PROPAGATOR FOR FERMION FIELD AND QUARK CONFINEMENT[J]. Chinese Physics C, 1981, 5(3): 273-281.

GAO CHONG-SHOU and RUAN TU-NAN. THE SPECTRAL REPRESENTATION OF PROPAGATOR FOR FERMION FIELD AND QUARK CONFINEMENT[J]. Chinese Physics C, 1981, 5(3): 273-281. shu

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Received: 1979-08-06
Revised: 1900-01-01

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1.
沈阳化工大学材料科学与工程学院沈阳 110142

THE SPECTRAL REPRESENTATION OF PROPAGATOR FOR FERMION FIELD AND QUARK CONFINEMENT

GAO CHONG-SHOU
RUAN TU-NAN

Received Date: 1979-08-06
Accepted Date: 1900-01-01
Available Online: 1981-06-05

Abstract: The properties of fermion causal Green's function is discussed according to the theory of spectral representation. The definition of effective mass is established from the view point of field theory, and the approximate expression of S_F' (p) as |p²|«M² and the asymptotic formula of S_F' (p) as p²→+∞ is given. In terms of these result the problem of quark confinement is discussed. We find that: (ⅰ) Based on the theory of spectral re presentation the concept of relative confinement is allowed, and if renormalization effect is strong, the quarks can demonstrate definitely lighter effective mass when they are far away from the mass shell; (ⅱ) Based on the theory of spectral representation the concept of absolute confinement is unallowable, even the absolute confinement is taken as the limit of relative confinement. That is if the concept of absolute confinement is introduced, we must discard a part of elementary hypothesis of spectral representation theory.