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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 particular, we shall consider the $e^2toinfty$ limit where the potential becomes confining. Within a bosonization approximation, effective Hamiltonians describing the low energy physics of the system are constructed, where we show that the system can be described as a fermi liquid formed by chargeless quasi-particles which has vanishing wavefunction overlap with the bare fermions in the system.
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 dimensio
In this thesis, we study the breakdown of the Fermi liquid state in cuprate superconductors using the renormalization group (RG). We seek to extend earlier work on the crossover from the Fermi liquid state to the pseudo gap phase based on RG flows in
We propose a Real-Space Gutzwiller variational approach and apply it to a system of repulsively interacting ultracold fermions with spin 1/2 trapped in an optical lattice with a harmonic confinement. Using the Real-Space Gutzwiller variational approa
We study the nature of many-body eigenstates of a system of interacting chiral spinless fermions on a ring. We find a coexistence of fermionic and bosonic types of eigenstates in parts of the many-body spectrum. Some bosonic eigenstates, native to th
We propose the use of an orthogonal wave packet basis to analyze the low-energy physics of interacting electron systems with short range order. We give an introduction to wave packets and the related phase space representation of fermion systems, and