Covariant Perturbation Theory (IV). Third Order in the Curvature

Understand

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.