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Covariant Perturbation Theory (IV). Third Order in the Curvature | | A. O. Barvinsky
; Yu. V. Gusev
; V. V. Zhytnikov
; G. A. Vilkovisky
; | | Date: |
6 Nov 2009 | | Abstract: | The trace of the heat kernel and the one-loop effective action for the
generic differential operator are calculated to third order in the background
curvatures: the Riemann curvature, the commutator curvature and the potential.
In the case of effective action, this is equivalent to a calculation (in the
covariant form) of the one-loop vertices in all models of gravitating fields.
The basis of nonlocal invariants of third order in the curvature is built, and
constraints arising between these invariants in low-dimensional manifolds are
obtained. All third-order form factors in the heat kernel and effective action
are calculated, and several integral representations for them are obtained. In
the case of effective action, this includes a specially generalized spectral
representation used in applications to the expectation-value equations. The
results for the heat kernel are checked by deriving all the known coefficients
of the Schwinger-DeWitt expansion including $a_3$ and the cubic terms of $a_4$.
The results for the effective action are checked by deriving the trace anomaly
in two and four dimensions. In four dimensions, this derivation is carried out
by several different techniques elucidating the mechanism by which the local
anomaly emerges from the nonlocal action. In two dimensions, it is shown by a
direct calculation that the series for the effective action terminates at
second order in the curvature. The asymptotic behaviours of the form factors
are calculated including the late-time behaviour in the heat kernel and the
small-$Box$ behaviour in the effective action. In quantum gravity, the latter
behaviour contains the effects of vacuum radiation including the Hawking
effect. | | Source: | arXiv, 0911.1168 | | Services: | Forum | Review | PDF | Favorites | |
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