2-LOOP QUANTUM-GRAVITY

被引:227
作者
VANDEVEN, AEM [1 ]
机构
[1] SUNY STONY BROOK, INST THEORET PHYS, STONY BROOK, NY 11794 USA
关键词
D O I
10.1016/0550-3213(92)90011-Y
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We prove the existence of a nonrenormalizable infinity in the two-loop effective action of perturbative quantum gravity by means of an explicit calculation. Our final result agrees with that obtained by earlier authors. We use the background-field method in coordinate space. combined with dimensional regularization and a heat kernel representation for the propagators. General covariance is manisfestly preserved. Only vacuum graphs in the presence of an on-shell background metric need to be calculated. We extend the background covariant harmonic gauge to include terms nonlinear in the quantum gravitational fields and allow for general reparametrizations of those fields. For a particular gauge choice and field parametrization only two three-graviton and six four-graviton vertices are present in the action. Calculational labor is further reduced by restricting to backgrounds, which are not only Ricci-flat, but satisfy an additional constraint bilinear in the Weyl tensor. To handle the still formidable amount of algebra. we use the symbolic manipulation program FORM. We checked that the on-shell two-loop effective action is in fact independent of all gauge and field redefinition parameters. A two-loop analysis for Yang-Mills fields is included as well, since in that case we can give full details as well as simplify earlier analyses.
引用
收藏
页码:309 / 366
页数:58
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