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博士一起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Stasheff博士在其早期研究中开发的技术，并结合Barnes博士的相关和互补专业知识，解决上同源物理学中的问题。这些技术可分为两大类：同调摄动理论和高阶同伦代数结构的研究。一种量化的方法是通过一种特殊的同调微扰理论。微扰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。本课题将进一步发展这种“强同伦李代数”的形式理论，并将其应用于物理。物理学中绝大多数BRST上同的例子都具有强同伦李代数的特征。该项目将通过Barnes博士对谱序列构造函数的描述来解决BRST上同性的表征。

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.