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 hyperboloidp; 2−m2; =0 is one-sheeted, as opposed to the case of bradyons wherep; 2+m2; =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.Facultad de Ciencias Exactas