Operator Modules, Quantum Groups and Quantum Information

算子模块、量子组和量子信息

• 批准号: RGPIN-2017-06275
• 负责人: Crann, Jason
• 金额: $ 1.53万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635290
• 关键词: Operator; Modules; Quantum; Groups; Information

In 1925 our view of the physical world drastically changed with the advent of Heisenberg's matrix mechanics. He showed that we may accurately describe quantum phenomena by interpreting time dependent variables as non-commuting matrices rather than functions. This "quantization" of functions, which underlies the theoretical development of quantum mechanics, has motivated mathematicians to quantize other areas of mathematics, including functional analysis, harmonic analysis, and information theory. The resulting areas: operator spaces, topological quantum groups, and quantum information theory, are, to this day, prominent world-wide research areas at the forefront of modern analysis and mathematical physics. They have all been shown to have a profound structure theory, and deep mathematical connections between them continue to emerge. My research program lies at the confluence of these three areas.

1925年，随着海森堡矩阵力学的出现，我们对物理世界的看法发生了巨大的变化。他表明，我们可以准确地描述量子现象的解释时间相依变量作为非交换矩阵，而不是功能。这种函数的“量子化”是量子力学理论发展的基础，也促使数学家们研究其他数学领域，包括泛函分析、调和分析和信息论。由此产生的领域：算子空间、拓扑量子群和量子信息理论至今仍是现代分析和数学物理学前沿的突出的世界性研究领域。它们都被证明具有深刻的结构理论，它们之间的深刻数学联系不断出现。我的研究计划是这三个领域的结合点。