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It is often preferable to work directly with these as they contain all the information that the full correlation functions contain since any disconnected diagram is merely a product of connected diagrams. By excluding other sets of diagrams one can define other correlation functions such as one-particle irreducible correlation functions.
Bubble diagrams, which result in the RPA when summed up. Solid lines stand for interacting or non-interacting Green's functions , dashed lines for two-particle interactions. The random phase approximation ( RPA ) is an approximation method in condensed matter physics and nuclear physics .
A bubble chart is a type of chart that displays three dimensions of data. Each entity with its triplet ( v 1 , v 2 , v 3 ) of associated data is plotted as a disk that expresses two of the v i values through the disk's xy location and the third through its size.
The Feynman diagram expansion may be obtained also from the Feynman path integral formulation. [3] The time-ordered vacuum expectation values of polynomials in φ, known as the n-particle Green's functions, are constructed by integrating over all possible fields, normalized by the vacuum expectation value with no external fields,
To produce simple poles on boson frequencies =, either of the following two types of Matsubara weighting functions can be chosen () = = = (+ ()),() = = (),depending on which half plane the convergence is to be controlled in. () controls the convergence in the left half plane (Re z < 0), while () controls the convergence in the right half plane (Re z > 0).
The phase space can also refer to the space that is parameterized by the macroscopic states of the system, such as pressure, temperature, etc. For instance, one may view the pressure–volume diagram or temperature–entropy diagram as describing part of this phase space. A point in this phase space is correspondingly called a macrostate.
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Such a diagram can be obtained from a connected tree diagram by taking two external lines of the same type and joining them together into an edge. Diagrams with loops (in graph theory, these kinds of loops are called cycles , while the word loop is an edge connecting a vertex with itself) correspond to the quantum corrections to the classical ...