Renormalization quantum field theory

It is not possible for conventional electromagnetic models of the electron to explain the observed property of a point charge with an excessively small radial dimension [20]. Nor does the divergence in self-energy of a point charge vanish in quantum field theory where the process of renormalization has been applied to solve the problem. 

In this connection there is an important question concerning the infinite selfenergy of a point charge in classical as well as in quantum field theory. The latter uses a renormalization process to solve the problem, namely, by subtracting two infinities to end up with a finite result. Despite the success of such a procedure, a more physically satisfactory way is needed [80]. Possibly the present theory may provide such an alternative, by tackling the divergence problem in a more surveyable manner. The finite result of a difference between two infinities due to renormalization theory would then be replaced by a finite result obtained from the product of an infinity and a zero, as demonstrated by the present analysis. 

Vol. 303 P. Breitenlohner, D. Maison, K. Sibold (Eds.), Renormalization of Quantum Field Theories with Non-linear Field Transformations. Proceedings, 1987. VI, 239 pages. 

Heitler spoke on the quantum theory of damping, which is a heuristic attempt to eliminate the infinities of quantum field theory in a relativistic invariant manner, Peierls spoke of the problem of self-energy, and Op-penheimer gave an account of the developments of the last years in electrodynamics in which he discussed the problem of the vacuum polarization and charge renormalization with special reference to the recent work of Schwinger and Tomonaga. 

For more recent developments, and especially for Landau-Ginzburg theory, see Zimmerman, W. (1970). Local operator product and renormalization in quantum field theory. Lectures on elementary particles and quantum field theory, Brandeis Summer Institute in Theoretical Physics (eds. S. Deser and M. Grisaru), p. 399. MIT Press, Cambridge, Mass. 

In this review an overview of the complete RDFT formalism is given. In Section 2 the relevant aspects of the underlying quantum field theory, i.e. QED with an additional static external potential characterizing the nuclei, are summarized. In particular, the question of renormalization is addressed for both... 

Approximation Methods in Quantum Mechanics, 1969 Nonlinear Plasma Theory, 1969 Quantum Kinematics and Dynamics, 1970 Statistical Mechanics A Set of Lectures, 1972 Photon-Hadron Interactions, 1972 Combinatorics and Renormalization in Quantum Field Theory, 1973... 

Many-Body Theories, Nuovo Cimento 49B, 1-31 (1967). H. Umezawa, Self-consistent Quantum Field Theory and Symmetry Breaking, in Renormalization and Invariance in Quantum Field Theory (E. R. Caianiello, ed.). Plenum Press, New York (1974), pp. 275-328. 

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