CONVENIENT VERSUS UNIQUE EFFECTIVE ACTION FORMALISM IN 2D DILATON-MAXWELL QUANTUM-GRAVITY

The structure of one-loop divergences of two-dimensional dilaton-Maxwe ll quantum gravity is investigated in two formalisms: one using a conv enient effective action and the other a unique effective action. The o ne-loop divergences (including surface divergences) of the convenient effetive action are calculated in three different covariant gauges: (i ) De Witt, (ii) OMEGA-degenerate De Witt, and (iii) simplest covariant . The on-shell effective action is given by surface divergences only ( finiteness of the S-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is discussed and classes of renor malizable dilaton and Maxwell potentials are found which coincide in t he cases of convenient and unique effective actions. A detailed compar ison of both situations, i.e. convenient vs. unique effective action, is given. As an extension of the procedure, the one-loop effective act ion in two-dimensional dilaton-Yang-Mills gravity is calculated.