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We use the term "BCS-Eliashberg-FL orthodoxy" in a narrow sense here to denote the theory of phonon-mediated pairing in conventional s-wave superconductors. A broader definition of the term could include various approaches based on spin fluctuations in nearly antiferromagnetic FL [P. Monthoux et al., Phys. Rev. Lett. 67, 3448 (1991)] which can lead to d-wave superconductivity.
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s as twice the conventional superfluid density; see Ref. 9.
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38
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84988785833
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note
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i(τ)), Eqs. (7) and (8), the magnetization vanishes with any choice of gauge.
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39
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84988746979
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note
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For the aficionados of gauge theories, this situation is reminiscent of the Landau gauge (∂·A = 0) being the fixed point among all covariant gauges of the Higgs-Abelian theory.
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40
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84988778782
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note
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μ(x), that the trouble arises.
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see Appendices A and B
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45
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84988764830
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note
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Irrelevant, but dangerously so, since it breaks the discrete symmetry of the fermion Lagrangian.
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48
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cond-mat/0110168 (unpublished)
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84988740996
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note
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We note that, superficially, Eq. (78) resembles a result one would obtain by decoupling the fermion fields from the line integral in Eq. (76) and then evaluated the latter in the leading-order cummulant expansion. However, it is easy to see that such a procedure would yield a wrong sign for F(r) and the resulting expression would not be gauge invariant. A more detailed consideration based on a careful treatment of gauge invariance (Ref. 44) leads to correct result, Eq. (78).
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58
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84988776669
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note
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3 itself-it might involve replacing the straight line integral with a more ramified path or a family of paths. Within our theory, however, it is clear that such a regularization ultimately reduces Eq. (76) to the original expression (73), with discrete vortex variables.
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59
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84988759097
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note
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This result was originally obtained by V.P. Gusynin (unpublished). We are indebted to him for generously sharing it with us and especially for drawing our attention to Ref. 44.
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84988776644
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References 51 and 52 quote a positive value for η′. We find that this is a result of an overall sign error and η′ should be negative, in agreement with Ref. 53. We are indebted to W. Rantner and D. V. Khveshchenko for communications regarding this issue and for their many insightful comments concerning gauge invariance.
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