  We reexamine the connection between spin and statistics through the
quantization of a complex scalar field, using the formulation with the property
that the hermitian conjugate of canonical momentum for a variable is just the
canonical momentum for the hermitian conjugate of the variable. Starting from
an ordinary Lagrangian density and imposing the anti-commutation relations on
the field, we find that the difficulty stems from not the ill-definiteness (or
unboundedness) of the energy and the breakdown of the causality but the
appearance of states with negative norms. It is overcome by introducing an
ordinary scalar field to form a doublet of fermionic symmetries, although the
system becomes empty leaving the vacuum state alone. These features also hold
for the system with a spinor field imposing the commutation relations on.
