  We construct the one-loop effective action in Yang-Mills and Pure Quantum
Gravity theories with heat kernel(or proper time method), which maintains
manifest covariance during and after quantization (gauge and diffeomorphism
invariance are always preserved). In this talk, we will basically focus on
"What, How, and Why" we prefer heat kernel than the standard Feynman diagram
calculation in momentum space at the one loop correction. The beta function of
Yang-Mills field in the fixed gravitational background can be more simply
obtained. The non-local term which cannot be easily obtained in the expansion
method are exactly computed in Yang-Mills in the case of covariantly constant
background field. The local term is consistent with asymptotic expansion method
or any most standard method. The non-local terms give some physical implication
concerning non-perturbative problems such as confinement and instabilities. The
modification of this technique to quantum gravity is discussed.
