  We construct the non-standard Lagrangian, called the multiplicative form, of
the homogeneous scalar field and fermion field through the inverse calculus of
variations, which the equation of motion still satisfies the Klein-Gordon and
Dirac equations, respectively. By employing the non-uniqueness of Lagrangian,
we show that the Lagrangians can be written between the linear combination of
standard and non-standard Lagrangian. The stability of the ghost field, an
unnatural smallness of cosmological constant, and the chiral condensate are
discussed by applying these new Lagrangians.
