  We show that for a wide class of Gaussian random fields, points are polar in
the critical dimension. Examples of such random fields include solutions of
systems of linear stochastic partial differential equations with deterministic
coefficients, such as the stochastic heat equation or wave equation with
space-time white noise, or colored noise in spatial dimensions $k\geq 1$. Our
approach builds on a delicate covering argument developed by M. Talagrand for
the study of fractional Brownian motion, and uses a harmonizable representation
of the solutions of these stochastic pde's.
