Quantum Gravity and Computer Symbolic Manipulation (Physics)

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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.