Evaluation of the Trace Anomaly in the U(1) Gauge Field Theory by Mathematica

概要

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A computational method by Mathematica developed by the author is extended to evaluate the trace anomaly for the U(1) gauge field in the gravitational background field. In the general covariant gauge, the differential operator in the exponent of the heat kernel becomes non-diagonal with respect to the Lorentz indices, and this makes the calculation complicated. The result agrees with Endo's one, and is dependent on the gauge parameter. The gauge dependence must be cancelled by adding a local counter term. Besides the DeWitt-Schwinger coefficients after taking the trace with respect to the Lorentz indices, we first present the gauge dependent DeWitt-Schwinger coefficients before taking the trace.
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