Abstract
In this chapter we consider how to implement RG ideas in the context of perturbation theory, and in a way which will be easier to generalize to other theories including gauge theories which we treat in the following chapter.
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Notes
- 1.
There is considerable freedom in choosing the way that the divergent terms are cancelled. These choices should be thought of as part of the regularization scheme. Different schemes correspond to different, but ultimately equivalent, parameterizations of the physical quantities in terms of the couplings in the action. This illustrates that we should not naïvely think of the \(g_i\) as physical quantities in themselves, rather they parametrize the physical quantities.
- 2.
At the one-loop level we can ignore wave-function renormalization. In addition, note that any other choice \(\mu =a\varphi \) for a constant \(a\ne 1\) is equivalent to \(a=1\) with a re-definition of the mass and coupling.
References
Coleman, S.R., Weinberg, E.J.: Radiative corrections as the origin of spontaneous symmetry breaking. Phys. Rev. D 7, 1888 (1973)
Collins, J.C: Renormalization. An Introduction to Renormalization, the Renormalization Group, and the Operator Product Expansion, p. 380. University Press, Cambridge (1984)
Peskin, M.E., Schroeder, D.V.: An Introduction to Quantum Field Theory. Addison-Wesley, Reading (1995)
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Hollowood, T.J. (2013). RG and Perturbation Theory. In: Renormalization Group and Fixed Points. SpringerBriefs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36312-2_3
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DOI: https://doi.org/10.1007/978-3-642-36312-2_3
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