Gauge-invariant response functions of fermions coupled to a gauge field

Details Gauge-invariant response functions of fermions coupled to a gauge field Gauge-invariant response functions of fermions coupled to a gauge field

1994-05-26

arxiv.org/abs/cond-mat/9405083v3

Physics

Condensed Matter

Plain Tex, 35 pages, 5 figures available upon request, Revised Version (Expanded discussion), To be published in Physical Revi

Scientific paper

10.1103/PhysRevB.50.17917

We study a model of fermions interacting with a gauge field and calculate gauge-invariant two-particle Green's functions or response functions. The leading singular contributions from the self-energy correction are found to be cancelled by those from the vertex correction for small $q$ and $\Omega$. As a result, the remaining contributions are not singular enough to change the leading order results of the random phase approximation. It is also shown that the gauge field propagator is not renormalized up to two-loop order. We examine the resulting gauge-invariant two-particle Green's functions for small $q$ and $\Omega$, but for all ratios of $\Omega / v_F q$ and we conclude that they can be described by Fermi liquid forms without a diverging effective mass.

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