Quantum Gravity and Computer Symbolic Manipulation (Physics)

计算机符号处理系统将被开发来处理出现在更高维、更高回路和更高阶引力理论中的许多最有趣的张量问题。使用极其强大的基于微处理器的科学工作站(在某些应用程序中，其速度可与超级计算机相媲美)，当前的符号处理语言将被扩展和补充，以执行量子引力和相关理论中非常详细的计算。作为一个例子，“符号运算”将被应用于所谓的热核技术的研究，这些技术用于计算重要的数学结构，如迹线和轴向反常、有效作用量、格林函数、指数定理、应力张量和其他相关对象。这样的计算必须以完美的精度完成，只有配备了特殊软件的高速计算机才可能实现，而不是目前存在于任何符号操作系统中的任何软件。可能必须应用人工智能技术来帮助物理学家分析可能的路径，以简化由此产生的非常大的表达式。

Computer symbolic manipulation systems will be developed to treat many of the most interesting tensorial problems that appear in higher-dimensional, higher-loop and higher-order theories of gravity. Using the extremely powerful microprocessor-based scientific work-stations (with speeds that rival supercomputers for some applications), current symbolic manipulation languages will be extended and supplemented to perform very detailed computations in quantum gravity and related theories. As one example, "symbol crunching" will be applied to the study of the so-called heat kernel techniques for computing important mathematical structures like trace and axial anomalies, effective action counterterms, Green's functions, index theorems, stress tensors and other related objects. Such computations, which must be done with perfect accuracy, are possible only with high-speed computers armed with special software beyond any that currently exists in any symbolic manipulation system. Artificial intelligence techniques may have to be applied to help the physicist with the analysis of the possible routes toward simplification of the very large expressions that result.