I discuss in this talk a bosonization approach recently developed. It leads to the (exact) bosonization rule for fermion currents in d > 2 dimensions and also provides a systematic way of constructing the bosonic action in different regimes.
The total number of states of any system is produced by all the possible interactions of the particles in that system. It follows therefore that there is need to obtain the states of the system before a model can be applied to it. Recently we developed a simple method to obtain the electronic states in the two electron lattice systems in all the three dimensions. This method encompasses rules formulated from a detailed study of each dimension. In the current study, the method will be extended to bosons which do not obey the Pauli exclusion principle like the electrons so that their interactions are different from those of the latter. The need for the extension of the method to bosons is also discussed in the work. Keywords: lattices, bosons, fermions, interactions, bosonic states Global Journal of Pure and Applied Sciences Vol. 12(1) 2006: 129-135
Inspired by the recent work by Delacretaz et. al. [Phys. Rev. Res. 4, 033131 (2022)], we rigorously derive an exact and simple method to bosonize a non-interacting fermionic system with a Fermi surface starting from a microscopic Hamiltonian. In the long-wavelength limit, we show that the derived bosonized action is exactly equivalent to the action obtained by Delacretaz et. al. In addition, we propose diagrammatic rules to evaluate correlation functions using our bosonized theory and demonstrate these rules by calculating the three- and four-point density correlation functions. We also consider a general density-density interaction and show that the simplest approximation in our bosonic theory is identical to RPA results.