Two-particle renormalizations in many-fermion perturbation theory: the importance of the Ward identity

2002/10/31 by V. Janis, V Janis
Physics and Astronomy · #Conservation law #Diagrammatic reasoning #Dynamical systems theory #Gravitational singularity #High-Energy Particle Collisions Research #Identity (music) #Particle physics theoretical and experimental studies #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Quantum Chromodynamics and Particle Interactions #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1088/0953-8984/15/21/102

published as J. Phys.:Condens. Matter 15 (2003) L311 · REVTeX4, 4 pages, 2 EPS figures

arxiv created 2002/11/05 · openalex publication_date 2003/05/16 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We analyse two-particle renormalizations within the many-fermion perturbation expansion. We show that present diagrammatic theories suffer from a lack of direct diagrammatic control over the physical two-particle functions. To rectify this, we introduce and prove a Ward identity enabling an explicit construction of the self-energy from a given two-particle irreducible vertex. Approximations constructed in this way are causal, obey conservation laws, and offer explicit diagrammatic control of singularities in dynamical two-particle functions.

Citations

• Stationary Entropy Principle and Renormalization in Normal and Superfluid Systems. I. Algebraic Formulation
• The Anderson-Mott transition
• Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons
• Asymptotic Limit of High Spatial Dimensions and Thermodynamic Consistence of Mean-Field Theories