Transfer function, renormalization

If there is no explicit external electromagnetic field, the covariant field equations determine a self-interaction energy that can be interpreted as a dynamical electron mass Sm. Since this turns out to be infinite, renormalization is necessary in order to have a viable physical theory. Field quantization is required for quantitative QED. The classical field equation for the electromagnetic field can be solved explicitly using the Green function or Feynman propagator GPV, whose Fourier transform is —gllv/K2, where k = kp — kq is the 4-momentum transfer. The product of y0 and the field-dependent term in the Dirac Hamiltonian, Eq. (10.3), is... 

The finite-size scaling theory combined with transfer matrix calculations had been, since the development of the phenomenological renormalization in 1976 by Nightingale [70], one of the most powerful tools to study critical phenomena in two-dimensional lattice models. For these models the partition function and all the physical quantities of the system (free energy, correlation length, response functions, etc) can be written as a function of the eigenvalues of the transfer matrix [71]. In particular, the free energy takes the form... 

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