Decomposition into one-particle irreducible Green functions in many-body physics
Résumé
Many-body physics can be considered as a quantum field theory (QFT) where the vacuum is replaced by a general quantum state. In quantum field theory, the vacuum expectation value of a normal product of creation and annihilation operators is always zero. This is no longer the case if the vacuum is replaced by a general state. As a consequence, the combinatorics of many-body physics is more complex than that of quantum field theory and the general theory has made very slow progress. In this work, an analysis of the Hopf algebraic structure of many-body physics is used to derive the structure of Green functions in terms of connected and one-particle irreducible Greeen functions.
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