Vacuum of the Quantum Yang-Mills Theory and Magnetostatics
Jul, 197818 pages
Published in:
- Nucl.Phys.B 143 (1978) 485-502
- Published: 1978
Report number:
- Print-78-0730 (PRINCETON)
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Abstract: (Elsevier)
It is argued that since in asymptotically free Yang-Mills theories the quantum ground state is not controlled by perturbation theory, there is no a priori reason to believe that individual orbits corresponding to minima of the classical action dominate the Euclidean functional integral. To examine and classify the vacua of the quantum gauge theory, we propose an effective action in which the gauge field coupling constant g is replaced by the effective coupling g (t), t = ln [ F μν a ) 2 μ 4 ] . The vacua of this model correspond to paramagnetism and perfect paramagnetism, for which the gauge field is F μν a = 0, and ferromagnetism, for which ( F μν a ) 2 = λ 2 , i.e. spontaneous magnetization of the vacuum occurs. We show that there are no instanton solutions to the quantum effective action. The equations for a point classical source of color spin are solved, and we show that the field infrared energy becomes linearly divergent in the limit of spontaneous magnetization. This implies bag formation, and an electric Meissner effect confining the bag contents.- FIELD THEORETICAL MODEL: YANG-MILLS
- GAUGE FIELD THEORY: VACUUM STATE
- GAUGE FIELD THEORY: MAGNETIC FIELD
- GAUGE FIELD THEORY: EUCLIDEAN
- GAUGE FIELD THEORY: PATH INTEGRAL
- GAUGE FIELD THEORY: INFRARED PROBLEM
- MODEL: MAGNET
- FIELD EQUATIONS: SOLITON
- MODEL: BAG
- QUARK: CONFINEMENT
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