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Dynamical symmetry breakings on a nontrivial topology
Song, DaeYup,Kim, JaeKwan 순천대학교 기초과학연구소 1991 基礎科學硏究誌 Vol.2 No.-
Dynamical symmetry breakings in two-dimensional massless fermion field theory with quartic interactions (the Gross-Neveu model) are investigated in the large-fermion-number (N) limit on a space with the S^1×S^1 topology which may correspond to the finite-volume system at finite temperature. Four types and the sum of the spin structures are considered. It is shown that the model has a richer phase structure in all boundary conditions than those in R^2 or R^1×S^1 space-time. It depends on the effective area and the ratio of the circumferences of the two circles whether or not dynamical symmetry breakings occur. In the sum of the spin structures, the phase diagram is the same as that of the periodic-periodic boundary condition and the critical line equation can be written in modular-invariant form.
Completeness of spin-3 field in two-boson free-field-realized conformal field theory
Song, DaeYup,Kim, JaeKwan 순천대학교 기초과학연구소 1991 基礎科學硏究誌 Vol.2 No.-
We consider the higher- (integer-)spin fields which can be realized with the derivatives of two-boson free fields in two-dimensional conformal quantum field theory. We show that the operator-product expansion (OPE) between higher-spin fields themselves cannot be closed when the spins are larger than 3. Thus, with the requirement of the closure of the OPE, the spin-3 field given by Fateev and Zamolodchikov is uniquely possible-that is, it is "complete." The same analyses on N-(≥3-) boson free-field-realized conformal field theories are discussed.
금융위기 이후 경제학의 새로운 분석도구로서의 복잡계 이론
이대엽,박하일 梨花女子大學校 社會科學大學 社會科學硏究所 2012 사회과학연구논총 Vol.28 No.-
복잡계 이론은 시스템 동학의 갑작스런 변화를 설명하고 이를 사전에 예측하기 위해 발전해 왔으며 이와 관련된 복잡계 이론의 연구들은 최근의 금융위기를 이해하는 데 새로운 시각을 제시한다. 복잡계 이론은 복잡계를 구성하는 개별 구성요소들보다는 개별 구성요소들 간의 복잡한 상호작용이 야기하는 출현적 현상에 주목한다는 점에서 금융 시스템에서의 출현적 현상인 시스템 리스크를 이해하는데 기여하고 있다. 복잡계 이론은 향후 다음과 같은 분야에서 활용도가 높아질 것으로 예상된다. 복잡 네트워크 이론은 시스템 리스크의 측정 등 거시건전성의 부문 간 차원을 이해하는 데 유용하며, 복잡계의 임계 전환(critical transition)은 거시건전성의 동태적 차원을 분석하는 데 활용될 수 있다. 또한 행위자 기반 모형(ABM)은 현실의 복잡한 측면들을 모형에 도입하고 경제주체의 제한된 합리성과 학습 등을 중시한다는 점에서 경제주체의 높은 합리성을 가정하고 있는 동태적․확률적 일반균형(DSGE) 모형과 상호 보완적 역할을 수행할 것으로 기대된다. Complex systems theory has been developed to explain sudden changes in system dynamics and to make ex-ante predictions on such changes. Relevant studies on this theory provide new perspectives for understanding the recent financial crisis. Complex systems theory help understand systemic risk which is an emergent phenomenon in a financial system, in that it focuses on the emergent property resulting from complex interactions among individual components rather than on each component comprising the complexity. The use of complex systems theory is expected to increase in areas as follows. First, complex networks theory is useful in understanding the cross-sectional aspect of macro-prudentiality like the evaluation of systemic risk. Second, the studies on the critical transition of complex systems can shed some light on the dynamic aspect of macro-prudentiality. Also, an Agent-Based Model (ABM) is expected to play complementary roles to a Dynamic Stochastic General Equilibrium (DSGE) model which assumes high rationality of economic agents, in that agent-based modeling includes complex aspects of the real world into the model and places importance on the bounded rationality and learning of economic agents.