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Superfluid Fermions: Partial Bosonization in the Particle–Particle Channel

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Introduction to the Functional Renormalization Group

Part of the book series: Lecture Notes in Physics ((LNP,volume 798))

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Abstract

While the decoupling of the fermionic two-body interaction in the forward scattering channel described in Chap. 11 is natural if the interaction involves only small momentum transfers, such a procedure is not appropriate for other types of interactions. For example, the superconducting instability of a normal metal is triggered by particle–particle scattering processes with vanishing total momentum, so that in this case a Hubbard–Stratonovich decoupling in the particle–particle channel is more natural. Of course, if the resulting mixed Bose–Fermi theory could be solved exactly, then the choice of the Hubbard–Stratonovich field should not matter. However, in practice one has to rely on approximations, so that it is important to introduce the physically relevant collective degrees of freedom from the beginning by means of a proper choice of the Hubbard–Stratonovich field. In fact, it is a priori not clear whether the physical properties of a given system can be simply described by means of a decoupling involving only a single Hubbard–Stratonovich field (Bartosch et al. 2009a). We shall further comment on multicomponent Hubbard–Stratonovich transformations in Sect. 12.6.

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  1. Goethe-Universität Frankfurt, Institut für Theoretische Physik, Max-von-Laue-Str. 1, 60438, Frankfurt, Germany

    Peter Kopietz, Lorenz Bartosch & Florian Schütz

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  1. Peter Kopietz
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Kopietz, P., Bartosch, L., Schütz, F. (2010). Superfluid Fermions: Partial Bosonization in the Particle–Particle Channel. In: Introduction to the Functional Renormalization Group. Lecture Notes in Physics, vol 798. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05094-7_12

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