  Following the canonical quantization procedure for a tachyon field, the usual
Hamiltonian and the creation and annihilation operators are obtained. The
observation that the mass hyperboloid $p^2-m^2=0$ is one-sheeted, as opposed to
the case of bradyons where $p^2+m^2=0$ is two-sheeted, leads to the
construction of a base which is unbounded for negative as well as for positive
energies. There is a zero-energy eigenfunction from which all other states can
be constructed by repeated application of decreasing or increasing operators,
within this Fock space the vacuum expectation value of the chronological
product of field operators is shown to coincide with Cauchy's principal-value
Green's function.
