Symmetry-improved CJT effective action
Symmetry-improved CJT effective action
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提高对称性的 CJT 有效作用
DOI：
10.1016/j.nuclphysb.2013.06.004
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
D. Teresi
中科院分区：
文献类型：
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作者：
A. Pilaftsis;D. Teresi
Cornwall、Jackiw 和 Tomboulis (CJT) 提出的形式主义提供了一种系统方法，可以一致地恢复量子热场理论中的非微扰效应。 CJT 有效作用的一个主要限制是其循环膨胀引入了可能的全局对称性的残余破坏，从而在理论的自发破缺阶段产生了大量的戈德斯通玻色子。在本文中，我们开发了一种新颖的对称性改进的 CJT 形式，用于在循环展开中一致地编码全局对称性。在我们的形式主义中，循环截断 CJT 有效动作的场和传播器的极值解受到由于全局对称性而由 Ward 恒等式给出的额外约束。通过考虑简单的 O(2) 标量模型，我们表明，与其他方法不同，我们的方法满足许多重要的场论属性。特别是，我们发现 O(2) 自发对称破缺产生的戈德斯通玻色子是无质量的，并且相变是二阶相变，已经在 Hartree-Fock 近似中。考虑到日落图后，我们展示了我们的方法如何正确描述环中无质量戈德斯通玻色子和希格斯粒子的阈值属性。最后，假设对 Hartree-Fock 近似 CJT 有效作用进行最小修改，我们计算相应的对称性改进的 CJT 有效势，并讨论其标量场值远离其最小值的唯一性的条件。
The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward Identities due to global symmetries. By considering a simple O(2) scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O(2) is massless and the phase transition is a second-order one, already in the Hartree–Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree–Fock approximated CJT effective action, we calculate the corresponding symmetry-improved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.