Many-Body Vacuum Diagrams and Their Recursive Graphical Construction

Abstract

The grand-canonical potential of many-body physics can be considered as a functional of the interaction-free correlation function. As such it obeys a nonlinear functional differential equation which can be turned into a recursion relation. This is solved graphically order by order in the two-particle interaction to find all connected vacuum diagrams with their proper weights. As a special case, the procedure is applied to generate the Hugenholtz diagrams for a weakly interacting Bose gas.

Author Information under http://www.physik.fu-berlin.de/~pelster/

References in corpus (4)

• T_c for homogeneous dilute Bose gases: a second-order result
• Functional Closure of Schwinger-Dyson Equations in Quantum Electrodynamics, Part 1: Generation of Connected and One-Particle Irreducible Feynman Diagrams
• Recursive Graphical Construction for Feynman Diagrams and Their Weights in Ginzburg-Landau Theory
• Recursive Graphical Construction of Tadpole-Free Feynman Diagrams and Their Weights in phi^4-Theory

Cited by in corpus (8)

• Critical Temperature of Weakly Interacting Dipolar Condensates
• Bose-Einstein Condensation Temperature of Dipolar Gas in Anisotropic Harmonic Trap
• Hedin's equations and enumeration of Feynman's diagrams
• Recursive Schr\" odinger Equation Approach to Faster Converging Path Integrals
• Enumeration of many-body skeleton diagrams
• Recursive Graphical Solution of Closed Schwinger-Dyson Equations in phi^4-Theory -- Part1: Generation of Connected and One-Particle Irreducible Feynman Diagrams
• A Table of Third and Fourth Order Feynman Diagrams of the Interacting Fermion Green's Function
• A novel approach to perturbative calculations for a large class of interacting boson theories