U.S.-Australia Cooperative Research on Cohomological Methodsin Mathematical Physics

该奖项支持北卡罗来纳大学教堂山分校的James D.Stasheff博士访问澳大利亚悉尼大学，与Donald Barnes博士合作研究数学物理中的上同调方法。研究人员将通过开发和应用斯塔谢夫博士在早期研究中开发的技术，以及巴恩斯博士相关和互补的专业知识，来解决上同源物理学中的问题。这些方法可分为两大类：同调摄动理论和高阶同伦代数结构的研究。量子化的一种方法是通过一种特殊的同调微扰理论。扰动微分中的项通常可以解释为高阶同伦结构。斯塔谢夫博士在数学物理的几个不同方面发现了这种结构的李代数版本。本项目将进一步发展这种“强同伦李代数”的形式理论，并将其应用于物理学。物理上的BRST上同调的绝大多数例子都具有强同伦李代数的特征。这个项目将通过Barnes博士的谱序列构建器的特征来描述BRST上同源性的特征。

This award supports a visit by Dr. James D. Stasheff of the University of North Carolina, Chapel Hill, to the University of Sydney, Australia, to work with Dr. Donald Barnes on cohomological methods in mathematical physics. The researchers will address problems in cohomological physics in terms of developing and applying techniques developed by Dr. Stasheff in his earlier research in combination with the relevant and complementary expertise of Dr. Barnes. These techniques fall into two broad categories: homological perturbation theory and the study of higher order homotopy algebraic structure. One approach to quantization is via a special kind of homological perturbation theory. The terms in a perturbed differential can often be interpreted as higher order homotopy structure. Dr. Stasheff identified a Lie algebra version of such structure in several different aspects of mathematical physics. This project will further develop the formal theory of such "strong homotopy Lie algebras" and apply it to the physics. The vast majority of examples of BRST cohomology in physics share the characteristic features of strongly homotopy Lie algebras. This project will address the characterization of BRST cohomology along the characterization of spectral sequence constructors by Dr. Barnes.