Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions
arXiv:2411.13857 · doi:10.1088/1751-8121/adc3de
Abstract
The paper studies a regularization of the quantum (effective) action for a scalar field theory in a general position on a compact smooth Riemannian manifold. As the main method, we propose the use of a special averaging operator, which leads to a quasi-locality and is a natural generalization of a cutoff regularization in the coordinate representation in the case of a curved metric. It is proved that the regularization method is consistent with a process of gluing of manifolds and partition functions, that is, with the transition from submanifolds to the main manifold using an additional functional integration. It is shown that the method extends to other models, and is also consistent with the process of multiplicative renormalization. Additionally, we discuss issues related to the correct introduction of regularization and the locality.
arXiv commentLaTeX, 30 pages, 1 figure. Firstly appeared in Russian, November 15, 2024, see https://www.pdmi.ras.ru/preprint/2024/24-11.html
References in corpus (19)
- Eta-Invariants and Determinant Lines
- Perturbative quantum gauge theories on manifolds with boundary
- Higher covariant derivative regularization revisited
- Operator Cutoff Regularization and Renormalization Group in Yang-Mills Theory
- Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams
- Two-Loop Cutoff Renormalization of 4-D Yang-Mills Effective Action
- The higher covariant derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories
- Formula for two-loop divergent part of 4-D Yang-Mills effective action
- Special Functions for Heat Kernel Expansion
- Two-loop renormalisation of gauge theories in Implicit Regularisation and connections to dimensional methods
- Explicit Cutoff Regularization in Coordinate Representation
- Quantum equation of motion and two-loop cutoff renormalization for model
- Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization
- Implicit Regularisation Technique: Calculation of the Two-loop -theory -function
- Construction of the unitary free fermion Segal CFT
- On Two-Loop Effective Action of 2D Sigma Model
- Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing
- Three-loop renormalization of the quantum action for a five-dimensional scalar cubic model with the usage of the background field method and a cutoff regularization
- Some Basic Tools of QFT