岐阜市立女子短期大学研究紀要　第53輯（平成16年3月）

抄録

Evaluation of the Third Heat Kernel Coefficient
in a Dirac Field Theory by Mathematica

Abstract

A computational method by Mathematica developed by the author is extended to evaluate the third coefficient of the heat kernel for the Dirac field in the gravitational background field. Eight-order derivative of the geodesic parallel displacement biscalar and sixth-order derivative of the geodesic bispinor in the coincidence limit are evaluated and their indices are contracted. The result of the third coefficient partly agrees with Gilkey's one, but there remains some discrepancy. The reason is not traceable at present.

キーワード : heat kernel, trace anomaly, chiral anomaly, graviational anomaly, Mathematica

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