Geodesic
Background field calculations in~quantum field theory (vacuum polarization)
Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 2, pp. 219-231

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A manifestly covariant technique for calculating the heat kernal asymptotic expansion is developed for the general case of arbitrary background fields and spaces. The first four coefficients of the asymptotic expansion which determine the vacuum polarization of massive quantum fields are explicitely calculated. 
@article{TMF_1989_79_2_a5,
     author = {I. G. Avramidi},
     title = {Background field calculations in~quantum field theory (vacuum polarization)},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {219--231},
     publisher = {mathdoc},
     volume = {79},
     number = {2},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_79_2_a5/}
}
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I. G. Avramidi. Background field calculations in~quantum field theory (vacuum polarization). Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 2, pp. 219-231. http://geodesic.mathdoc.fr/item/TMF_1989_79_2_a5/