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Inspired by the recent work by Delacretaz et. al., we rigorously derive anexact and simple method to bosonize a non-interacting fermionic system with aFermi surface starting from a microscopic Hamiltonian. In the long-wavelengthlimit, we show that the derived bosonized action is exactly equivalent to theaction obtained by Delacretaz et. al. In addition, we propose diagrammaticrules to evaluate correlation functions using our bosonized theory anddemonstrate these rules by calculating the three- and four-point densitycorrelation functions. We also consider a general density-density interactionand show that the simplest approximation in our bosonic theory is identical toRPA results.

An exact method for bosonizing the Fermi surface in arbitrary dimensions