Quantum fluctuations in afield theory. I. Stability of the vacuum
- 15 August 1975
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 12 (4), 1071-1088
- https://doi.org/10.1103/physrevd.12.1071
Abstract
We study the effect of quantum fluctuations in a field theory using a Hartree-type approximation. We reduce the operator field equations into a set of coupled -number (infinite in number) equations. We show that these equations can also be derived from a variational principle. We carry out the renormalization procedure in the one-dimensional theory in detail and demonstrate how the renormalization can be done in a fashion consistent with the Hartree approximation. We then apply the technique to study the effective potential and the stability of the vacuum. We find that the abnormal vacuum is unstable as the coupling becomes strong, and a transition between the abnormal () and the normal () vacua occurs in both the one- and the three-dimensional theory. A generalization of the theory to include internal symmetries is briefly outlined.
Keywords
This publication has 27 references indexed in Scilit:
- Quark bags and local field theory. II. Confinement of Fermi and vector fieldsPhysical Review D, 1975
- Particle spectrum in model field theories from semiclassical functional integral techniquesPhysical Review D, 1975
- Heavy quarks and strong binding: A field theory of hadron structurePhysical Review D, 1975
- Nonperturbative methods and extended-hadron models in field theory. II. Two-dimensional models and extended hadronsPhysical Review D, 1974
- Nonperturbative methods and extended-hadron models in field theory. I. Semiclassical functional methodsPhysical Review D, 1974
- Nonperturbative methods and extended-hadron models in field theory. III. Four-dimensional non-Abelian modelsPhysical Review D, 1974
- Baryon structure in the bag theoryPhysical Review D, 1974
- Quark "bags" and local field theoryPhysical Review D, 1974
- New extended model of hadronsPhysical Review D, 1974
- Effective mass and correlation length of nucleon constituentsLettere al Nuovo Cimento (1971-1985), 1972