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The surface counter-terms of the ϕ44 theory on the half space R+×R3.
- Source :
-
Journal of Mathematical Physics . Feb2024, Vol. 65 Issue 2, p1-54. 54p. - Publication Year :
- 2024
-
Abstract
- In a previous work, we established perturbative renormalizability to all orders of the massive ϕ 4 4 -theory on a half-space also called the semi-infinite massive ϕ 4 4 -theory. Five counter-terms which are functions depending on the position in the space, were needed to make the theory finite. The aim of the present paper is to establish that for a particular choice of the renormalization conditions the effective action consists of a part which is independent of the boundary conditions (Dirichlet, Neumann and Robin) plus a boundary term in the case of the Robin and Neumann boundary conditions. The key idea of our method is the decomposition of the correlators into a bulk part, which is defined as the scalar field model on the full space R 4 with a quartic interaction restricted to the half-space, plus a remainder which we call "the surface part." We analyse this surface part and establish perturbatively that the ϕ 4 4 theory in R + × R 3 is made finite by adding the bulk counter-terms and two additional counter-terms to the bare interaction in the case of Robin and Neumann boundary conditions. These surface counter-terms are position independent and are proportional to ∫Sϕ2 and ∫Sϕ∂nϕ. For Dirichlet boundary conditions, we prove that no surface counter-terms are needed and the bulk counter-terms are sufficient to renormalize the connected amputated (Dirichlet) Schwinger functions. A key technical novelty as compared to our previous work is a proof that the power counting of the surface part of the correlators is better by one scaling dimension than their bulk counterparts. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 65
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 175796351
- Full Text :
- https://doi.org/10.1063/5.0164178