Abstract
By introducing the phase transformation of electron operators, we map the equation of motion of an one-particle Green's function into that of a non-interacting one-particle Green's function where the electrons are moving in a time-depending scalar potential and pure gauge fields for a D-dimensional electron gas, and we demonstrate that the electronic correlation strength strongly depends upon the excitation energy spectrum and collective excitation modes of electrons. It naturally explains that the electronic correlation strength is strong in the one dimension, while it is weak in the three dimensions.
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