ManyBody Quantum Field Theory: Phenomenology and Applications to Crystals
TITLE 
ManyBody Quantum Field Theory: Phenomenology and Applications to Crystals 
STAFF 
Massimo Ladisa, Valerio Olevano*, Markus Holtzmann*, GianMarco Rignanese*, Lucia 
CNR MODULE 
Department: ICT (Information and Communication Technology) 
KEYWORDS 
1. Electronic properties of materials 
COLLABORATIONS 
Institut NéelCNRS (http://neel.cnrs.fr), Laboratoire des Solides IrradiésEcole PolytechniqueCNRS (http://www.lsi.polytachnique.fr), Laboratoire de Physique Théorique de la Matière CondenséeUniv.PMCurieCNRS (http://www.lptmc.jussieu.fr) European Theoretical Spectroscopy Facility (http://www.etsf.eu), Unité de PhysicsChimie et de Physique de MatériauxUCLouvainlaNeuve (http://www.pcpm.ucl.ac.be) 
DESCRIPTION 
Green's function theory, also called (improperly) ManyBody Perturbation Theory (MBPT), is a Quantum Field Theory based on a formalism of second quantization of operators. The fundamental degree of freedom is the Green's function or propagator, which represents the probability amplitude for the propagation of an electron. As in any other quantum field theory (for example QED), the manybody system can be expanded in perturbation theory, with the coupling being the manybody interaction term. The Green's function (as well as any other quantity of the theory, such as the selfenergy or the polarization) can be calculated at a given order of perturbation theory. A Feynman diagrammatic analysis is hence possible. The theory at the first order is equivalent to HartreeFock theory.However the coupling is not small (compare to, for example, the electronion interaction) and the expansion does not converge. The second order is not necessarily smaller than the first. Hence one needs to resort to more complicated methods to solve the theory, such as partial resummations of diagrams at all orders, or better, iterative methods. In iterative schemes one introduces new quantities into the theory but relating them to the old, in the hope that at the end one can succeed in closing the equations. Indeed, MBPT can be solved thanks to a set of five integrodifferential equations, called the Hedin equations, that have to be solved iteratively until selfconsistency is achieved. So far, nobody has solved the Hedin equations for a real system. Approximations are required to simplify the problem. Among the most widely used approximate schemes are the GW approximation for the selfenergy and the BetheSalpeter Equation approach and its related approximations. (Source: www.etsf.eu) 
CONTACTS 
Massimo Ladisa, PhD
