  Introducing collective variables, a collective description of nuclear surface
oscillations has been developed with the first quantized language, contrary to
the second quantized one in Sunakawa's approach for a Bose system. It overcomes
difficulties remaining in the traditional theories of nuclear collective
motions: Collective momenta are not exact canonically conjugate to collective
coordinates and are not independent. On the contrary to such a description,
Tomonaga first gave the basic idea to approach elementary excitations in a
one-dimensional Fermi system. The Sunakawa's approach for a Fermi system is
also expected to work well for such a problem. In this paper, on the $isospin$
space, we define a density operator and further following Tomonaga, introduce a
collective momentum. We propose an $exact$ canonically momenta approach to a
one-dimensional neutron-proton (N-P) system under the use of the Grassmann
variables.
