Dynamical Symmetry Breaking in Curved Spacetime : Four-Fermion Interactions
Dynamical Symmetry Breaking in Curved Spacetime : Four-Fermion Interactions
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DOI：
10.1143/ptps.127.93
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发表时间：
1997-09
影响因子：
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通讯作者：
T. Inagaki;T. Muta;S. Odintsov
中科院分区：
文献类型：
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作者：
T. Inagaki;T. Muta;S. Odintsov
本文综述了弯曲时空中的四费米子相互作用理论。从D维Minkowski时空（2-D-4）出发，计算了1/N展开式首阶有效势，并研究了该理论的相结构。用同样的方法计算了四费米子模型中复合算符的有效势：a）D维弱弯曲时空（线性曲率近似），B）D维de Sitter宇宙和反de Sitter宇宙，c）D维Einstein宇宙.理论的相结构的分析以及数值研究。曲率引起的相变进行了讨论，费米子质量动态生成。作为四费米子模型的推广，我们考虑了弱弯曲时空中的规范Nambu-Jona-Lasinio（NJL）模型、高阶导数NJL模型和超对称NJL模型，其中有效势是解析计算的.再次分析了模型的相结构，给出了规范NJL模型手征对称性破缺的解析条件。最后分析了两种外部效应（非零温度和引力场、非平凡拓扑和引力场以及磁场和引力场）对四费米子模型相结构的影响。曲率和温度诱导或曲率和拓扑诱导相变的可能性进行了讨论。我们还认为，由于引力场的存在，被弱磁场破坏的手征对称性可以恢复。本文还简要讨论了四费米子模型在量子引力中的应用。该论文发表在Prog。Theor. 127（1997）93.
This review deals with the theory of four-fermion interactions in curved spacetime. Starting with the D-dimensional Minkowski spacetime (2� D � 4) the effective potential in the leading order of 1/N-expansion is calculated and the phase structure of the theory is investigated. Using the same technique the effective potential for composite operatorin four-fermion models is calculated under the following circumstances: a) D-dimensional weakly curved spacetime (in linear curvature approximation), b) D-dimensional de Sitter and anti-de Sitter universe, c) D-dimensional Einstein universe. The phase structure of the theory is investigated analytically as well as numerically. Curvature induced phase transitions are discussed where fermion masses are dynamically generated. As an extension of four-fermion models we consider the gauged Nambu-Jona-Lasinio (NJL) model, higher derivative NJL model and supersymmetric NJL model in weakly curved spacetime where the effective potential is analytically evaluated. The phase structure of the models is again analyzed and the condition for the chiral symmetry breaking in the gauged NJL model is given in an analytical form. Finally the influence of two external effects (non-zero temperature and gravitational field, non- trivial topology and gravitational field as well as magnetic and gravitational field) to the phase structure of four-fermion models is analyzed. The possibility of curvature and temperature-induced or curvature- and topology-induced phase transitions is discussed. It is also argued that the chiral symmetry broken by a weak magnetic field may be restored due to the presence of gravitational field. Some applications of four-fermion models in quantum gravity are also briefly investigated. This paper was published in Prog. Theor. Phys. Suppl. 127 (1997) 93.