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6 Renormalized Perturbation Theories of the First Kind
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Published:July 1990
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Abstract
In discussing renormalized perturbation theories (RPTs), we shall divide them into two categories. We shall then devote a separate chapter to each of these categories. Firstly, in this chapter we will concentrate on those theories which are not compatible with the Kolmogorov inertial-range spectrum. These can be thought of as the older theories although, in point of strict chronological order, this is not true of every case. Secondly, in Chapter 7, after first turning our attention to the problems involved in finding an analytical theory which does have the Kolmogorov spectrum as its solution, we then consider those theories which can claim to have achieved that result. Questions concerning the significance of one or other category will be deferred until Chapter 8, where we shall attempt to make an overall assessment of the various theories. The theories which we are just about to discuss in the present chapter can again be subdivided, but this time on the basis of the general approach to the problem. That is, there are those theories which are based on a direct manipula-tion of the equations of motion and there are those which work with the probability distribution of the fluctuating velocities. Loosely speaking, we could refer to the first as a ‘Chapter 5’ type of theory, and the second as a ‘Chapter 4’ type of theory. We shall discuss the work of Krishnan (1959), as representing the first type, and the work of Edwards (1964), as representing the second.
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