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1.3 A road map

The remainder of this article is organized in the following way:

Section 2 about effective field theories does not involve gravity at all, but instead first describes why effective field theories are useful in other branches of physics. The discussion is kept concrete by considering a simple toy model, for which it is argued how some applications make it useful to keep track of how small ratios of energy scales appear in physical observables. In particular, considerable simplification can be achieved if an expansion in small energy ratios is performed as early as possible in the calculation of low-energy observables. The theoretical tool for achieving this simplification is the effective Lagrangian, and its definition and use is briefly summarized using the toy model as an explicit example.

Section 3, which deals with quantum gravity as an effective theory, describes how the tools of the previous section may be applied to calculating quantum effects including the gravitational field. In particular, it is shown how to make predictions despite general relativity’s non-renormalizability, since effective Lagrangians are generically not renormalizable. As we shall see, however, some of the main results one would like to have regarding the size of quantum corrections to arbitrary loop orders remain incomplete.

In Section 4 explicit applications of these ideas are described in this section, which use the above results to compute quantum corrections to several gravitational results for two kinds of sources. These calculations compute the leading quantum corrections to Newton’s Law between two slowly-moving point particles, and to the gravitational force between two cosmic strings (both in 3 + 1 spacetime dimensions).

In the final Section 5 conclusions are briefly summarized.

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