Transport, Noise, and Conservation in the Electron Gas: How to Build a Credible Mesoscopic Theory

The Boltzmann-Landau-Silin and Landauer-Buettiker-Imry theories of electron transport are shown to be mutually incompatible. The first respects microscopic gauge invariance, electron-hole symmetry, and the conserving sum rules for the correlated electron gas. The second approach does not. That is directly evident in its unphysical compressibility.