By Peter Kopietz

The writer provides intimately a brand new non-perturbative method of the fermionic many-body challenge, enhancing the bosonization procedure and generalizing it to dimensions *d*1 through sensible integration and Hubbard--Stratonovich alterations. partly I he essentially illustrates the approximations and obstacles inherent in higher-dimensional bosonization and derives the best relation with diagrammatic perturbation conception. He exhibits how the non-linear phrases within the power dispersion might be systematically integrated into bosonization in arbitrary *d*, in order that in *d*1 the curvature of the Fermi floor could be taken under consideration. half II provides purposes to difficulties of actual curiosity. The publication addresses researchers and graduate scholars in theoretical condensed topic physics.

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**Extra info for Bosonization of Interacting Fermions in Arbitrary Dimensions**

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This approximation is correct to leading order in qc /kF , and becomes exact in the limit qc /kF → 0. Note that this limit is approached either at high densities, where kF → ∞ at constant qc , or in the limit that the range qc of the effective interaction in momentum space approaches zero while kF is held constant. It follows that, up to higher order corrections in qc /kF , the vertex Un (q1 α1 . . qn αn ) is diagonal in all patch labels, Un (q1 α1 . . qn αn ) = δ α1 α2 · · · δ α1 αn Unα1 (q1 .

E. fqαα = fq , such as the long-range tail of the Coulomb interaction), we may identify the entire momentum space with a single sector. In other words, there is no need any more for subdividing the degrees of freedom into several sectors. 6 Summary and outlook 31 case the problem of around-the-corner processes is solved trivially. However, given the fact that our main interest is the calculation of the single particle Green’s function in the vicinity of the Fermi surface, it is still advantageous to work with a coordinate system centered on the Fermi surface, as shown in Fig.

39)) ψk† ψk+q . 13) αα′ where for q = 0 ′ Π αα (q) = β 1 βV β = V β dτ 0 dτ ′ e−iωm (τ −τ ′ ) 0 ′ ′ T ρˆα ρα q (τ )ˆ −q (τ ) ′ α D {ψ} e−Smat {ψ} ρα q ρ−q D {ψ} e−Smat {ψ} . 14) We shall refer to Π(q) as the global or total density-density correlation func′ tion, and to Π αα (q) as the local or sector density-density correlation function. 14) reduces to ′ Π0αα (q) = − 1 V ′ Θα (k)Θα (k + q) k f (ξk+q ) − f (ξk ) ξk+q − ξk − iωm By relabeling k + q → k it is easy to see that . 15) 36 3. Hubbard-Stratonovich transformations ′ ′ Π0αα (q) = Π0α α (−q) .