  We summarize recent developments in the field of higher dimensional
bosonization made by the authors and collaborators and propose a general
formula for the field operator in terms of currents and densities in one
dimension using a new ingredient known as a `singular complex number'.
  Using this formalism, we compute the Green function of the homogeneous
electron gas in one spatial dimension with short-range interaction leading to
the Luttinger liquid and also with long-range interactions that leads to a
Wigner crystal whose momentum distribution computed recently exhibits essential
singularities.
  We generalize the formalism to finite temperature by combining with the
author's hydrodynamic approach. The one-particle Green function of this system
with essential singularities cannot be easily computed using the traditional
approach to bosonization which involves the introduction of momentum cutoffs,
hence the more general approach of the present formalism is proposed as a
suitable alternative.
