Hierarchy of Self-Consistent Approximate Methods and the Parquet ...
Hierarchy of Self-Consistent Approximate Methods and the Parquet ...
Hierarchy of Self-Consistent Approximate Methods and the Parquet ...
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Green function <strong>and</strong> self-energy<br />
(x 2 , t 2 )<br />
(x 1 , t 1 )<br />
• 1-particle Green function G<br />
ψ(x 2 , t 2 ) = ∫ G(x 2 , t 2 ; x 1 , t 1 )ψ(x 1 , t 1 ) dx 1 dt 1<br />
⊲ amplitude (phase) accumulated when a particle moving around some path<br />
⊲ long-ranged<br />
• self-energy Σ<br />
⊲ renormalization due to <strong>the</strong> interaction with o<strong>the</strong>r particles<br />
⊲ short-ranged<br />
• Similarly, we can define 2-partilce Green function <strong>and</strong> 2-particle “self-energy” (vertex).<br />
<strong>Hierarchy</strong> <strong>of</strong> <strong>Self</strong>-<strong>Consistent</strong> <strong>Approximate</strong> <strong>Methods</strong> <strong>and</strong> <strong>the</strong> <strong>Parquet</strong> Formalism 5