  This paper is concerned with the smoothness (in the sense of Meyer-Watanabe)
of the local times of Gaussian random fields. Sufficient and necessary
conditions for the existence and smoothness of the local times, collision local
times, and self-intersection local times are established for a large class of
Gaussian random fields, including fractional Brownian motions, fractional
Brownian sheets and solutions of stochastic heat equations driven by space-time
Gaussian noise.
