2024/04/03 by Upalaparna Banerjee, Banerjee, Upalaparna, Joydeep Chakrabortty +3 · 2 citations
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #High-pressure geophysics and materials #Quantum Chromodynamics and Particle Interactions #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.2404.02734
openalex publication_date 2024/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We outline a proposal, based on the Heat-Kernel method, to compute 1PI effective action up to any loop order for quantum field theory with scalar and fermion fields. We algebraically extract the divergences associated with the composite 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: (i) real singlet scalar, and (ii) complex fermion-scalar interacting theories. 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 for extracting infrared divergence in massless limits.