2009/04/30 by Bruno Gonçalves, Bruno Goncalves, Guilherme de Berredo-Peixoto +1
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Numerical methods for differential equations #Quantum chaos and dynamical systems #hep-th
paper · pdf · doi:10.1142/s0217751x10049669
published as Int.J.Mod.Phys.A25:2382-2390,2010 · A small section on decoupling theorem added
arxiv created 2009/05/24 · openalex publication_date 2010/04/30 · arxiv updated 2010/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The well-known formula det (A · B) = det A · det B can be easily proved for finite dimensional matrices but it may be incorrect for the functional determinants of differential operators, including the ones which are relevant for Quantum Field Theory applications. Considerable work has been done to prove that this equality can be violated, but in all previously known cases the difference could be reduced to renormalization ambiguity. We present the first example, where the difference between the two functional determinants is a nonlocal expression and therefore can not be explained by the renormalization ambiguity. Moreover, through the use of other even dimensions we explain the origin of this difference at qualitative level.