Abstract
The aim of this chapter is to present methods for improving the convergence properties of the perturbation theory. In particular, the influence of new energy scales appearing when one embeds a field theory into a specific environment might require critical analysis of the formal perturbation series, since infrared (IR) divergences might be generated by the new scale. The chapter begins with a discussion of the origin of IR singularities. It is followed by the presentation of the general optimization strategy and the question of the renormalizability of optimized series. The detailed implementation of the strategy will be illustrated with the example of the one-component ϕ 4-theory. In the second half of the chapter, an enlarged perturbative framework will be introduced when a static resummation is not satisfactory, and a momentum-dependent resummation is needed. This is accomplished by the two-particle-irreducible (2PI) approximation, which is understood in our interpretation also as a specific example of resummation.
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Notes
- 1.
Often, IR problems appear only as enhanced contributions and not actual divergences. Nevertheless, we will call them “IR divergences.”
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Jakovác, A., Patkós, A. (2016). Optimized Perturbation Theory. In: Resummation and Renormalization in Effective Theories of Particle Physics. Lecture Notes in Physics, vol 912. Springer, Cham. https://doi.org/10.1007/978-3-319-22620-0_4
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DOI: https://doi.org/10.1007/978-3-319-22620-0_4
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