ABSTRACT
This chapter provides a microscopic basis to the phenomenological understanding of Landau Fermi liquids. It examines the effect of electron density fluctuations on the Stoner instability, particularly to understand their effect on the mean-field condition for the instability. The temperature dependence coming from the distribution functions in the numerator has a characteristic scale of the order of the Fermi energy. Ward identities provide relations between the self-energy and the vertex functions, thus bridging the phenomenological and microscopic aspects. The microscopic justification of this assumption rests on Ward identities. The ideas of scaling theory, developed in the context of classical critical phenomena, can be generalized to the quantum case. Thus vertex corrections, through their relation to the Ward identity for the self-energy, enable to provide a microscopic justification of one of the key assumptions of Landau Fermi liquid theory.
