https://doi.org/10.1140/epjp/s13360-024-05491-7
Regular Article
Renormalization of scalar and fermion interacting field theory for arbitrary loop: Heat–Kernel approach
Indian Institute of Technology Kanpur, 208016, Kalyanpur, Kanpur, Uttar Pradesh, India
Received:
6
April
2024
Accepted:
24
July
2024
Published online:
10
August
2024
We outline a proposal, based on the Heat–Kernel method, to compute the counter terms up to any loop order for quantum field theory with scalar and fermion fields including higher mass dimensional operators. We algebraically extract the divergences associated with the omposite operators without explicitly performing any momentum loop integral. We perform this analysis explicitly for one and two-loop cases and pave the way for three-loop as well. Using our prescription we compute the two-loop counter terms for a theory containing higher mass dimensional effective operators that are polynomial in fields for two different cases having: (i) real singlet scalar, and (ii) complex fermion. We also discuss how the minimal Heat–Kernel fails to deal with the effective operators involving derivatives. We explicitly compute the one-loop counter terms for such a case within an O(n) symmetric scalar theory employing a non-minimal Heat–Kernel. Our method computes the counter terms of the composite operators directly, and is also useful to extract infrared divergence in massless limit.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
