Quasiparticle wave function and its equation of motion

The quasiparticle wave function of a many-electron system is traditionally defined as the eigenfunction of the quasiparticle eigenvalue equation involving the self-energy. In this article a different concept of a quasiparticle wave function is derived from the general definition of the Green's function without reference to self-energy. The proposed quasiparticle wave function can decay in time, and in contrast to the traditional one it contains not only the main quasiparticle mode but also other modes due to coupling to collective excitations in the system. In the recently developed dynamical exchange-correlation potential formalism, this definition of a quasiparticle wave function leads to an equation of motion with an effective field, which appears to have a simple form expected to be amenable to realistic approximations. A simple model for the effective potential is proposed which is suitable for materials whose valence electrons are dominated by itinerant <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>s</a:mi><a:mtext>−</a:mtext><a:mi>p</a:mi></a:mrow></a:math> electrons such as simple metals.