By Rudolf Haussmann
This learn monograph bargains an advent to complicated quantum box theoretical concepts for many-particle platforms past perturbation conception. a number of schemes for resummation of the Feynman diagrams are defined. The ensuing approximations are specially compatible for strongly correlated fermion and boson platforms. additionally thought of is the crossover from BCS superconductivity to Bose--Einstein condensation in fermion platforms with powerful beautiful interplay. particularly, a box theoretic formula of "bosonization" is gifted; it truly is released the following for the 1st time. this system is utilized to the fractional quantum corridor impact, to the Coulomb plasma, and to numerous precisely solvable types.
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Extra info for Self-consistent quantum field theory and bosonization for strongly correlated electron systems
45) via Z,' defined in ,,,2 the fermions are described by the quadratic occurs A. in the Scaling The Dyson equation. 46). Equivalently, the three parameters may be 1 T, nF, and aF where nF is the fermion density. 47) are scaling invariant. All quantities may be rescaled by the density nF. To do this we need the Fermi wave number kF (37r 2nF) 113 for the length scale and the Fermi as h'k/2rn energy scale. 51) into (3-44)-(3-47), we obtain four dimensionless selfconsistent equations for the scaling functions.
These pairs and develop a macroscopic quantum coherence. e. (Tf,,. (rl, tl)Tf,2 (r2, t2)), which becomes below T,. nonzero particles because However, usually the fermion pairs are the interaction need not be very strong. The pairs may be large and penetrate each other. Cooper has shown (Cooper 1956) that in a weakly interacting Fermi gas already an infinitesimal small attractive interaction is not well defined sufficient for the formation of a bound pair. Based on this observation the superconductivity Bardeen-Cooper-Schrieffer theory (BCS theory) been developed (Bardeen, Cooper, and Schrieffer 1957, of see has also Schrieffer liquid formed, supposed the temperature is sufficiently small.
3c. This symmetric vertex is invariant under perby the bare vertex function Fig. mutations of the four external lines and identified To according to Fig. 3d. 1) is spin independent, in the field theoretic considerations the spin indices need not be treated explicitly. Due to the special structure of the elementary vertex in Fig. 7) occur. 7) with respect to the spin indices will be retained under summations and matrix multiplications. Hence we may omit the spin indices and reduce all considerations to the 2 x 2 matrix matrices.
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