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).

拟议的研究项目位于保形场理论领域 - 在共同组下，二维量子场理论不变 - 在字符串理论，统计模型（临界点）和凝结物理学中具有应用。研究的主要研究是提供共形场理论的准粒子公式。在这样的框架中，希尔伯特空间是通过按限制规则填充国家排除原则的限制规则来描述了希尔伯特空间的。该方法产生许多新颖的角色公式（状态的生成函数），它们具有极大的内在数学兴趣（例如，对著名的罗杰斯 - 拉马努扬身份的新概括）。