By Peter Kopietz

The writer provides intimately a brand new non-perturbative method of the fermionic many-body challenge, enhancing the bosonization strategy and generalizing it to dimensions *d*1 through practical integration and Hubbard--Stratonovich differences. partially I he in actual fact illustrates the approximations and barriers inherent in higher-dimensional bosonization and derives the correct relation with diagrammatic perturbation thought. He exhibits how the non-linear phrases within the strength dispersion should be systematically integrated into bosonization in arbitrary *d*, in order that in *d*1 the curvature of the Fermi floor might be taken under consideration. half II supplies purposes to difficulties of actual curiosity. The ebook addresses researchers and graduate scholars in theoretical condensed topic physics.

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Note that in this case |k −kα | assumes the smallest possible value. to choose the sectors as large as possible in order to avoid corrections due to the around-the-corner processes. 59)) should be well-defined. If these conditions are satisfied, we may use our formalism to calculate the single-particle Green’s function G(k α + q, i˜ ωn ) for all wave-vectors q that are small compared with the sector cutoffs. e. fqαα = fq , such as the long-range tail of the Coulomb interaction), we may identify the entire momentum space with a single sector.

Qn αn ) is diagonal in all patch labels, Un (q1 α1 . . qn αn ) = δ α1 α2 · · · δ α1 αn Unα1 (q1 . . 7) with Unα (q1 . . +qn ,0 i β n 1 n! n) k × G0 (k)G0 (k + qP2 ) · · · G0 (k + qP2 + . . + qPn ) . 6) as the diagonal-patch approximation. It is important to note that at finite qc /kF this approximation can only become exact in d = 1, because in this case the Fermi surface consists of two widely separated points. Except for special cases (see Chap. 7), in higher dimensions the covering of the Fermi surface involves always some adjacent patches, which can be connected by arbitrarily small momentum-transfers q.

7. Subdivision of the entire momentum space of a two-dimensional system with a spherical Fermi surface (thick solid circle) into sectors. The solid arrows point to the origins kα of local coordinate systems associated with the sectors. Note that only for sectors at the Fermi surface we may choose kα such that ǫkα = µ. For example ǫk2 = µ, but ǫk1 and ǫk3 are different from µ. k3 k2 k1 q k k (a) α (b) Fig. 8. (a) Spherical Fermi surface and wavevector k close to the Fermi surface. (b) If we are interested in G(k, i˜ ωn ), we choose the coordinate origin kα such that k = kα +q, with q parallel to kα .