Implicit regularization beyond one-loop order : scalar field theories.
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2007
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Implicit regularization (IR) has been shown as a useful momentum space tool for
perturbative calculations in dimension-specific theories, such as chiral gauge,
topological and supersymmetric quantum field theoretical models at one-loop
level. In this paper, we aim at generalizing systematically IR to be applicable
beyond one-loop order. We use a scalar field theory as an example and pave
the way for the extension to quantum field theories which are richer from the
symmetry content viewpoint. Particularly, we show that a natural (minimal)
renormalization scheme emerges, in which the infinities displayed in terms
of integrals in one internal momentum are subtracted, whereas infrared and
ultraviolet modes do not mix and therefore leave no room for ambiguities.
A systematic cancellation of the infrared divergences at any loop order takes
place between the ultraviolet finite and divergent parts of the amplitude for
non-exceptional momenta leaving, as a by-product, a renormalization group
scale.
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PONTES, C. R. et al. Implicit regularization beyond one-loop order: scalar field theories. Journal of Physics G: Nuclear and Particle Physics, v. 34, n. 10, p. 2215–2234, 2007. Disponível em: <https://iopscience.iop.org/article/10.1088/0954-3899/34/10/011>. Acesso em: 10 mar. 2020.