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The two known non-perturbative theories of localization in disordered wires,the Fokker-Planck approach due to Dorokhov, Mello, Pereyra, and Kumar, and thefield-theoretic approach due to Efetov and Larkin, are shown to be equivalentfor all symmetry classes. The equivalence had been questioned as a result offield-theoretic calculations of the average conductance by Zirnbauer [PRL 69,1584 (1992)], which disagreed with the Fokker-Planck approach in the symplecticsymmetry class. We resolve this controversy by pointing to an incorrectimplementation of Kramers degeneracy in these calculations, and we derivemodified expressions for the first two conductance moments which agree wellwith existing numerical simulations from the metallic into the localizedregime. ***Submitted to Physical Review B.***

Quantum transport in disordered wires: Equivalence of the one-dimensional σ model and the Dorokhov-Mello-Pereyra-Kumar equation