Analytic solution of Hedin's equations in zero dimensions
Abstract
Feynman diagrams for the manybody perturbational theory are enumerated by solving the system of Hedin's equations in zero dimension. We extend the treatment of Molinari [Phys. Rev. B 71, 113102 (2005)] and give a complete solution of the enumeration problem in terms of Whittaker functions. An important relation between the generating function of the electron propagator and anomalous dimension in quantum field theory of massless fermions and mesons in four dimensions (Yukawa theory) is found. The Hopf algebra of undecorated rooted trees yields the anomalous field dimension in terms of the solution of the same differential equation. Its relation to the mathematical problem of combinatorics of chord diagrams is discussed; asymptotic expansions of the counting numbers are obtained.
 Authors:
 Department of Physics, Kaiserslautern University of Technology, Box 3049, 67653 Kaiserslautern (Germany)
 Publication Date:
 OSTI Identifier:
 20929702
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 5; Other Information: DOI: 10.1063/1.2728512; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; ANALYTICAL SOLUTION; ANOMALOUS DIMENSION; DIFFERENTIAL EQUATIONS; ELECTRONS; FEYNMAN DIAGRAM; FUNCTIONS; MANYBODY PROBLEM; MESONS; PERTURBATION THEORY; PROPAGATOR; QUANTUM FIELD THEORY
Citation Formats
Pavlyukh, Y., and Huebner, W.. Analytic solution of Hedin's equations in zero dimensions. United States: N. p., 2007.
Web. doi:10.1063/1.2728512.
Pavlyukh, Y., & Huebner, W.. Analytic solution of Hedin's equations in zero dimensions. United States. doi:10.1063/1.2728512.
Pavlyukh, Y., and Huebner, W.. Tue .
"Analytic solution of Hedin's equations in zero dimensions". United States.
doi:10.1063/1.2728512.
@article{osti_20929702,
title = {Analytic solution of Hedin's equations in zero dimensions},
author = {Pavlyukh, Y. and Huebner, W.},
abstractNote = {Feynman diagrams for the manybody perturbational theory are enumerated by solving the system of Hedin's equations in zero dimension. We extend the treatment of Molinari [Phys. Rev. B 71, 113102 (2005)] and give a complete solution of the enumeration problem in terms of Whittaker functions. An important relation between the generating function of the electron propagator and anomalous dimension in quantum field theory of massless fermions and mesons in four dimensions (Yukawa theory) is found. The Hopf algebra of undecorated rooted trees yields the anomalous field dimension in terms of the solution of the same differential equation. Its relation to the mathematical problem of combinatorics of chord diagrams is discussed; asymptotic expansions of the counting numbers are obtained.},
doi = {10.1063/1.2728512},
journal = {Journal of Mathematical Physics},
number = 5,
volume = 48,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}

MaxwellDirac equations with zero magnetic field and their solution in two space dimensions
Under the assumption of a vanishing magnetic field (curl A = 0), a transformation of variables is exhibited which uncouples the MaxwellDirac equations. It is then shown that the Cauchy problem in two space dimensions has a unique solution for C/sup infinity/ data with compact support. 
Hedin's equations and enumeration of Feynman diagrams
Hedin's equations are solved perturbatively in zero dimension to count Feynman graphs for selfenergy, polarization, propagator, effective potential and vertex function in a manybody theory of fermions with twobody interaction. Counting numbers are also obtained in the GW approximation.