1992/06/26 by D. M. McAvity, D.M. McAvity, H. Osborn · 57 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Boundary conformal field theory #Boundary value problem #Conformal map #Curvature #Heat kernel #Neumann boundary condition #Perturbation theory (quantum mechanics) #Quantum Electrodynamics and Casimir Effect #Quantum field theory #Scalar (mathematics) #Scalar field #cond-mat
paper · pdf · doi:10.1016/0550-3213(93)90229-i
published in Nuclear Physics B 394(3), 728-788 (Elsevier BV) · 50 pages, DAMTP/92-31
arxiv created 1992/06/26 · openalex publication_date 1993/04/01 · openalex created_date 2016/06/24 · arxiv updated 2016/08/30 · openalex updated_date 2026/08/05
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed Dirichlet and Neumann boundary conditions. The method is applied to a general renormalisable scalar field theory in four dimensions using dimensional regularisation to two loops and expanding about arbitrary background fields. Detailed results are also specialised to an O(n) symmetric model with a single coupling constant. Extra boundary terms are introduced into the action which give rise to either Dirichlet or generalised Neumann boundary conditions for the quantum fields. For plane boundaries the resulting renormalisation group functions are in accord with earlier results but here the additional terms depending on the extrinsic curvature of the boundary are found. Various consistency relations are also checked and the implications of conformal invariance at the critical point where the β function vanishes are also derived. The local Scrödinger equation for the wave functional defined by the functional integral under deformations of the boundary is also verified to two loops. Its consistency with the renormalisation group to all orders in perturbation theory is discussed.