Phase Transition in the Nonlinear Sigma Model in Two + Epsilon Dimensional Continuum
Phase Transition in the Nonlinear Sigma Model in Two + Epsilon Dimensional Continuum
复制标题
二维 Epsilon 维连续体非线性 Sigma 模型中的相变
DOI：
10.1103/physrevd.14.985
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发表时间：
1976
影响因子：
5
通讯作者：
R. Shrock
中科院分区：
文献类型：
--
作者：
W. Bardeen;Benjamin W. Lee;R. Shrock
研究了2+e维非线性O（N）σ模型的相变。我们的分析是连续统理论，并不依赖于一个格的技巧。这种相变发生在耦合常数λc的临界值，这是重整化群的紫外稳定不动点。在“低温”阶段，O（N）对称性是以N−1个无质量的π介子非线性地实现的。通过求解大N极限下的理论，到1 N的首阶，我们证明了在“高温”相，π介子获得质量，出现了一个新粒子σ，它是π介子的束缚态，并与π介子简并。此外，通过对生成泛函的一般最速下降近似和显式计算，证明了这个上相是完全O（N）对称的，并且可以用线性σ-模型拉格朗日量来描述。证明了该理论的么正性，并讨论了与量子色动力学中夸克禁闭的类比。我们证明了理论的可重整化性，特别注意分离红外和紫外发散。
We study the phase transition in the nonlinear O(N) σ model in 2+e dimensions. Our analysis is of the continuum theory and does not rely upon the artifice of a lattice. This phase transition occurs at a critical value of the coupling constant λc, which is an ultraviolet-stable fixed point of the renormalization group. In the "low temperature" phase the O(N) symmetry is realized nonlinearly with N−1 massless pions. By solving the theory in the large-N limit, to leading order in 1N, we show that in the "high temperature" phase the pions gain mass and there appears a new particle, σ, which is a bound state of the π's and is degenerate with them. Furthermore, by a general steepest-descent approximation to the generating functional and by explicit calculations it is shown that this upper phase is fully O(N) symmetric and can be described by a linear σ-model Lagrangian. The unitarity of the theory is demonstrated and analogies with quark confinement in quantum chromodynamics are discussed. We prove the renormalizability of the theory, taking special care to separate infrared and ultraviolet divergences.