From Conformal Field Theory to Quantum Mechanics and Quantum Information

***我建议在理论物理的两个重要课题上进行研究：共形场论（CFT）和量子力学（QM）。我在这两个领域的目标是提高理论理解，从而为已知和新的物理应用铺平道路。****CFT是一门丰富而深刻的学科，具有许多物理应用。CFTs描述临界系统，弦的世界表，量子杂质问题，并且是其他物理量子场论的非摄动可解模型。****理解CFT的许多进展，包括我的许多贡献，都来自Wess-Zumino-Witten （WZW）模型和相关系统的研究。保持这种方法，我的目标是在分数水平上研究WZW模型，作为对数cft的原型；研究WZW熔合的相模型实现。****量子力学是物理学的基础。我的方法是从非标准的角度研究简单的系统，以提取更普遍适用的新见解。****相空间QM是我研究的一个（相对）不常见的观点，并打算继续研究。此外，我的目标是概括我过去在接触相互作用的重整化群分析方面的工作，以及在离散化凹室中研究QM。****除了继续我在CFT和QM方面的研究项目外，我计划通过在量子信息理论（QI）中启动一条新的研究路线，将重点从CFT转移到QM。由于它与量子计算的联系，以及它对量子力学基础的启发，量子力学目前是一个非常令人兴奋的主题。我的CFT背景给了我在QI中罕见的观点，以及应该被证明有用的技术。例如，量子边际问题在QI中是至关重要的，因为它的目标是理解复合系统的子系统的可能状态。在这方面，我在CFT中使用的许多工具都发挥了重要作用。***在短期内，我正在研究复正交设计的QI应用，从长远来看，我计划研究量子边际性与约简系统开放动力学之间的关系。****我的建议描述了一个战略组合，包括可靠的、富有成果的研究来源和新的、令人兴奋的工作。它为各级高素质人才的重要培训创造了机会，并促进了阿尔伯塔省（埃德蒙顿和卡尔加里分别有对CFT和QI感兴趣的强大团体），加拿大以及其他地区的合作。*** **

***I propose to perform research in two important topics in theoretical physics: conformal field theory (CFT) and quantum mechanics (QM). My objective in both areas is to improve theoretical understanding, thereby paving the way to physical applications, both known and new.****CFT is a rich and deep subject, with many physical applications. CFTs describe systems at criticality, the world sheets of strings, quantum impurity problems, and are non-perturbatively solvable models for other physical quantum field theories. ****Much progress in understanding CFT, including many of my contributions, has come from the study of Wess-Zumino-Witten (WZW) models and related systems. Maintaining that approach, I aim to study the WZW models at fractional level, as prototypes of logarithmic CFTs; and investigate the phase model realizations of WZW fusion. ****QM is fundamental in physics. My approach is to study simple systems, from non-standard points of view, to extract new insights that apply more generally. ****Phase-space QM is one (relatively) uncommon point of view that I study, and intend to continue to examine. In addition, I aim to generalize my past work on the renormalization-group analysis of contact interactions, as well as investigate QM in a discretized alcove.****In addition to continuing my research programs in CFT and QM, I plan to shift emphasis from CFT to QM, by initiating a new line of investigation in the theory of quantum information (QI). Due to its connection with quantum computation, and the light it has shone on the fundamentals of QM, QI is currently a very exciting theme. ***My background in CFT gives me a point of view that is rare in QI, and techniques that should prove useful. For example, the quantum marginal problem is crucial in QI, since its goal is to understand the possible states of a subsystem of a composite system. In this area many of the tools I have exploited in CFT have played important roles. ***In the short term, I am studying the QI uses of complex orthogonal designs, and in the longer term, I plan to investigate the relation between quantum marginality and the open dynamics of reduced systems. ****My proposal describes a strategic mix of reliable sources of fruitful research, and new, exciting work.   It creates the opportunity for significant training of highly-qualified personnel at all levels and facilitates collaboration in Alberta (there are strong groups in Edmonton and Calgary with interests in CFT and QI, respectively), Canada, and beyond.*** *** **