Quantum Gravity and Computer Symbolic Manipulation (Physics)

计算机符号处理系统将被开发， 处理许多最有趣的张量问题， 在更高维度、更高循环和更高阶的理论中， 重力 使用极其强大的基于微处理器 科学工作站（速度可与超级计算机相媲美 对于某些应用程序）、当前的符号操作语言 将得到扩展和补充，以执行非常详细的 量子引力和相关理论的计算。 作为一个 例如，“符号运算”将应用于研究 所谓的热核技术，用于计算重要的 数学结构，如轨迹和轴向异常，有效 作用量反项，绿色函数，指标定理，应力 张量和其他相关对象。 这样的计算，必须 要做到完美的准确性，是可能的，只有高速 配备有特殊软件的计算机， 存在于任何符号操作系统中。 人工 智能技术可能必须应用于帮助 物理学家分析了可能的路线， 简化了由此产生的庞大表达式。

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.