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This review is a summary of my work (partially in collaboration with Kurt Schoenhammer) on higher-dimensional bosonization during the years 1994-1996. It has been published as a book entitled Bosonization of interacting fermions in arbitrary dimensions by Springer Verlag (Lecture Notes in Physics m48, Springer, Berlin, 1997). I have NOT revised this review, so that there is no reference to the literature after 1996. However, the basic ideas underlying the functional bosonization approach outlined in this review are still valid today.
We study in this paper the properties of a gas of fermions interacting {em via} a scalar potential $v(q)=4pi{e}^2/q^2$ for $q<Lambda<<k_F$ at dimensions larger than one, where $Lambda$ is a high momentum cutoff and $k_F$ is the fermi wave vector. In
We construct fixed point lattice models for group supercohomology symmetry protected topological (SPT) phases of fermions in 2+1D. A key feature of our approach is to construct finite depth circuits of local unitaries that explicitly build the ground
Novel controlled non-perturbative techniques are a must in the study of strongly correlated systems, especially near quantum criticality. One of these techniques, bosonization, has been extensively used to understand one-dimensional, as well as highe
An unbiased zero-temperature auxiliary-field quantum Monte Carlo method is employed to analyze the nature of the semimetallic phase of the two-dimensional Hubbard model on the honeycomb lattice at half filling. It is shown that the quasiparticle weig
We investigate the 1D interacting two-component Fermi gas with arbitrary polarization. Exact results for the ground state energy, quasimomentum distribution functions, spin velocity and charge velocity reveal subtle polarization dependent quantum effects.