A new algebraic approach for calculating the heat kernel in quantum gravity

It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e., in symmetric spaces, may be presented in the form of an averaging over the Lie group of isometries with some nontrivial measure. Using this representation, the heat kernel diagonal, i.e., the heat kernel in coinciding points is obtained. Related topics concerning the structure of symmetric spaces and the calculation of the effective action are discussed.