  We consider the long standing problem in field theories of bosons that the
boson vacuum does not consist of a `sea', unlike the fermion vacuum. We show
with the help of supersymmetry considerations that the boson vacuum indeed does
also consist of a sea in which the negative energy states are all "filled",
analogous to the Dirac sea of the fermion vacuum, and that a hole produced by
the annihilation of one negative energy boson is an anti-particle. Here, we
must admit that it is only possible if we allow --as occurs in the usual
formalism anyway-- that the "Hilbert space" for the single particle bosons is
not positive definite. This might be formally coped with by introducing the
notion of a double harmonic oscillator, which is obtained by extending the
condition imposed on the wave function. This double harmonic oscillator
includes not only positive energy states but also negative energy states. We
utilize this method to construct a general formalism for a boson sea analogous
to the Dirac sea, irrespective of the existence of supersymmetry. The physical
result is consistent with that of the ordinary second quantization formalism.
We finally suggest applications of our method to the string theories.
