Vertex, diagrammatic representations

Fig. 1. Diagrammatic representation of single components of the synthon. The vertex from A is represented by a heavy dot whereas the virtual vertex from Wis represented by an open circle. The edge [ , o ] ([o, w]) is represented by a continuous line connecting the vertex o with the vertex o (vv). The loop [o, o] is represented by a continuous line beginning and ending at the same vertex v...

Fig. 1 (a) Self-energy in diagrammatic representation, (b) Expansion series for the vertex E up to g. Thick solid, thick dashed, and thin dashed lines indicate, respectively, the electron Green s function, the dressed phonon, and the bare phonon propagators... 

Fig. 7,3. Diagrammatic representation the collision process contributing to the repeated ring operator Each vertex represents an elastic collision between A and S the propagation between these correlating collisions is given by sequences of uncorrelated collisions of A with S and S with S.

Figure 4. Interacting vertexes in diagrammatic representation. The Latin indexes denote field components, the Greek indexes denote replicas.

Figure 5. The one-loop contributions to the one-particle irreducible vertex function r J k) in the diagrammatical representation.

Figure 3.3. Diagrammatic representation of B, C, D AB v CD) N X XgXj X( in which the lines directed towards the interaction vertex correspond to annihilation operators, whilst lines directed away from the interaction correspond to creation operators.

Resummation of asymptotic series The and y-functions are calculated perturbatively as series in the couplings Aj. The order of the expansion corresponds to the number of loops in the diagrammatic Feynman representation of the vertex functions (69). However, due to the (asymptotic) divergence of the RG functions series [84], one cannot directly derive reliable physical information... 

Following Kim [62] we consider the so-called faithful representation of the familiar Feynman diagrams [4], representing the vertexes with coupling constants uq, Vq, which describe the interaction of the fields diagrammatically, as is shown in Fig. 4. Here... 

---