  The fundamental solution for the wave equation in n variables is built from
the simple one-dimensional formula, via an integral representation of the
cosine of the sum of squares of self-adjoint operators. Representation formulas
are given both in the commutative and non-commutative case. The formulas are
illustrated for the wave equation as well as for the Klein-Gordon equati on. As
examples for the non-commuting case, we discuss the harmonic oscillator and
simple sum of squares hypoelliptic operators such as the Grushin operator and
the Heisenberg Laplacian.
