Interaction vertex

Figure 1. The main diagram for the —> ujir° decay, (W) weak-interaction vertex.

The photon-nucleus interaction vertex is described by the Dirac (Fi) and Pauli (T2) form factors... 

Hence, at low momenta the photon-nucleus interaction vertex (after the Foldy-Wouthuysen transformation and transition to the two-component nuclear spinors) is described by the expression... 

Since each additional interaction vertex in the cluster expansion contributes two segment summations and one momentum integral, with these substitutions a total factor of n2 d = neaccompanies the additional excluded... 

Fig. 2. These diagrams represent (a) Dyson equation for diffusion propagator, (b) interaction vertex dressed by impurity and intergranular scattering, (c) Screened Coulomb interaction.

Similar ladder diagrams describe the dressing of interaction vertex as it shown in Fig. 2b. The dressed vertex can be used to obtain the polarization operator, that defines effective dynamically screened Coulomb interaction... 

The Fourier representation of the anharmonic propagator is obtained from Eqs. (73) and (72), by using Wick s theorem (69), together with the Fourier representation of the harmonic phonon propagators. The time integrations can then explicitly be performed, yielding the condition 2,- w, = 0 and a factor /3 at every interaction vertex. 

Fig. 33. (a) Dyson equation for the pseudofermion propagators of CEF states n, m (broken lines). Phonons are indicated by wavy lines. Open circles represent the magnetoelastic interaction vertex, (b) Bubble diagram for the dynamical magnetic susceptibility using renormalized propagators. Open squares represent the dipolar operator J. 

Here, the replica interaction vertex g x) is the correlation function with Fourier image (26). 

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

As it follows from the general field theory, a divergence can be eliminated by subtraction of the counterterms from the mass and interaction vertex. If we define the variations a and g by... 

Each interaction vertex between states p> and q in iny diagram... 

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.

With these definitions, it is very easy to draw the diagram corresponding to a given term of the expansion (41) reading a contribution from right to left (i.e. in the arrow of time), the lines of the initial state p ipl 0) are first represented then each of the interactions which lead the system to the intermediate states k", (k ". .. are indicated by the corresponding elementary vertex of Fig. 3 until the final state k is reached. These vertices are ordered from right to left. 

The last term is introduced within the self-consistent Hartree approximation (within the functional up to one vertex), //// = 10/9 accounts different coefficients in functional for the self-interaction terms (ri4 - for the given field d and dla)2 d )2 terms), cf [20], We presented da = 2k d t>ke lkfix, ... 

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