Articles written in Pramana – Journal of Physics
Volume 69 Issue 4 October 2007 pp 639-650 Research Articles
We summarize recent developments in the ﬁeld of higher dimensional bosonization made by Setlur 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 lead 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.
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