摘要
By means of the optimized expansion technique, the D + 1-dimensional quantum sine-Gordon （sG） field theory is studied nonperturbatively for both zero and finite temperatures.In 1 + 1 and 2+ 1 dimensions, the theory is finite when momentum cutoff Λ tends to infinity.The temperature-dependent Coleman phase transition conditions we obtained reduce to theknown results g<sub>cr</sub><sup>2</sup> =8π for 1+ 1 dimensions and g<sub>cr</sub><sup>2</sup>= 16π/m<sub>RO</sub> for 2+ 1 dimensions whenT→0. Especially, g<sub>cr</sub> tends to zero at T→∞ limit both for 1 + 1 and 2 + 1 dimensions. Thereis no critical temperature making the Φ= 0 vacuum unstable. In 3 + 1 dimensions, if g<sup>2</sup> isfinite and Λ→∞, the theory is trivial. There is no nontrivial "precarious" phase for the3+ 1-dimensional sG model. The effective potential for the "autonomous" phase has asimilar form as the classical potential and the temperature effects only make contribution tothe infinitesimal part of this phase.
By means of the optimized expansion technique, the D + 1-dimensional quantum sine-Gordon (sG) field theory is studied nonperturbatively for both zero and finite temperatures.In 1 + 1 and 2+ 1 dimensions, the theory is finite when momentum cutoff Λ tends to infinity.The temperature-dependent Coleman phase transition conditions we obtained reduce to theknown results g_(cr)~2 =8π for 1+ 1 dimensions and g_(cr)~2= 16π/m_(RO) for 2+ 1 dimensions whenT→0. Especially, g_(cr) tends to zero at T→∞ limit both for 1 + 1 and 2 + 1 dimensions. Thereis no critical temperature making the Φ= 0 vacuum unstable. In 3 + 1 dimensions, if g^2 isfinite and Λ→∞, the theory is trivial. There is no nontrivial 'precarious' phase for the3+ 1-dimensional sG model. The effective potential for the 'autonomous' phase has asimilar form as the classical potential and the temperature effects only make contribution tothe infinitesimal part of this phase.
基金
Project supported by the National Natural Science Foundation of China.
