NONDEGENERATE CRITICAL POINTS, MORSE-DARBOUX LEMMA AND PROPAGATORS IN BV FORMALISM

The notion of nondegenerate critical point in the BV formalism is studied. The analogs of the Morse and Darboux theorems in the BV formalism are proven. The theorem on the normal form of an arbitrary quadratic function on odd symplectic space is proven. This can be viewed as an analog of Jordan type decomposition for a pair of a symmetric pairing on vector space and an anti-symmetric pairing on the dual space. The last result was used for the construction of propagators in the BV formalism in the equivariant setting, see [2, 3, 4]