Absence of noncanonical modification in the balance equation theory of resistivity

Abstract

Relative electron momenta p i ′ and coordinates r i ′, introduced in the balance equation theory of resistivity, are constrained and obey noncanonical commutation relations [r′ iα, p′ jβ]= iδ αβ(δ ij− N l . Thus it is improper to use them as translation generation. Nevertheless the contribution to the frictional force from the noncanonical 1/N term is exactly cancelled by that arising from the noncommutability of the center-of-mass coordinates R( t) at different times, such that the relative electrons can be treated as an unconstrained, canonical system and the center-of-mass as a classical single particle in the calculation of the resistivity of the system.