Conformal field theory and integrable systems

共形场论和可积系统

• 批准号: 9027-2008
• 负责人: Mathieu, Pierre
• 金额: $ 3.28万
• 依托单位: Université Laval
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=474486
• 关键词: Conformal; field; theory; integrable; systems

The proposed research project is in the area of conformal field theory - a two-dimensional quantum field theory invariant under the conformal group - which has applications in string theory, statistical models (critical point) and condensed matter physics. The main line of research is to provide a quasi-particle formulation of conformal field theories. In such a framework, the Hilbert space is described by filling the space of states by quasi-particles subject to restriction rules that generalize the Pauli exclusion principle. This method produces many novel character formulae (the generating functions for states), which are of great intrinsic mathematical interest (e.g., new generalizations of the famous Rogers-Ramanujan identities).

提议的研究项目是在共形场论领域-共形群下的二维量子场论不变量-在弦理论，统计模型（临界点）和凝聚态物理中有应用。研究的主线是提供共形场理论的准粒子表述。在这样的框架中，希尔伯特空间被描述为由服从于推广泡利不相容原理的限制规则的准粒子填充状态空间。这种方法产生了许多新颖的特征公式（状态的生成函数），这些公式具有很大的内在数学意义（例如，著名的罗杰斯-拉马努金恒等式的新推广）。