## Functional integral methods in the study of critical fluctuations in superconductors |

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Aslamazov and Larkin becomes biquadratic approximation bQ(t C+(t calculation coefficients coherence length condensation conn critical fluctuations current-current correlation function defined dependence diagram dimensional dirty limit diverge equal numbers equation equilibrium expansion factor Fermi surface fluctuation free energy Fourier fourth order term free energy functional frequency functional integral method Gaussian Ginzburg-Landau theory given Green's function Hamiltonian Hence identical imaginary impurity scattering interaction picture Marcelja mean field approximation mean field theory mean square fluctuations neglect non-zero notation Note obtain ODLRO order parameter pairing particle partition function Qm Qm quantity r-ip region renormalized temperature shift resp result specific heat superconductor t-matrix approximation t(Qm T>TcQ tanh thermodynamic limit thermodynamic potential tion transformation vanishes variables Qm vertex vertex function wavevector zero