136211 20260217205551.0 doi 10.1016/j.geomphys.2024.105264 sideral 139100 ART-2024-139100 eng Alonso, José Luis Universidad de Zaragoza (orcid)0000-0003-0694-155X Geometric flavors of Quantum Field theory on a Cauchy hypersurface. Part I: Gaussian analysis and other mathematical aspects 2024 Access copy available to the general public Unrestricted In this series of papers we aim to provide a mathematically comprehensive framework to the hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the point of differential geometry in infinite dimensions. In this first part we introduce the tools of Gaussian analysis in infinite dimensional spaces of distributions. These spaces will serve the basis to understand the Schrödinger and Holomorphic pictures, over arbitrary Cauchy hypersurfaces, using tools of Hida-Malliavin calculus. Here the Wiener-Ito decomposition theorem provides the QFT particle interpretation. Special emphasis is done in the applications to quantization of these tools in the second part of this paper. We devote a section to introduce Hida test functions as a notion of second quantized test functions. We also analyze of the ingredients of classical field theory modeled as distributions paving the way for quantization procedures that will be analyzed in [3]. info:eu-repo/grantAgreement/ES/AEI/PID2021-123251NB-I00 info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es 1.2 2024 MATHEMATICS 84 / 492 = 0.171 2024 Q1 T1 PHYSICS, MATHEMATICAL 39 / 61 = 0.639 2024 Q3 T2 0.616 2024 Geometry and Topology 2024 Q2 Physics and Astronomy (miscellaneous) 2024 Q2 Mathematical Physics 2024 Q2 3.2 2024 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Bouthelier-Madre, Carlos (orcid)0000-0003-1697-5710 Clemente-Gallardo, Jesús Universidad de Zaragoza (orcid)0000-0003-4721-7381 Martínez-Crespo, David Universidad de Zaragoza (orcid)0000-0002-6044-0337 2004 405 Universidad de Zaragoza Dpto. Física Teórica Área Física Teórica 203 (2024), 105264 [25 pp.] J. geom. phys. JOURNAL OF GEOMETRY AND PHYSICS 0393-0440 700617 http://zaguan.unizar.es/record/136211/files/texto_completo.pdf Versión publicada 1757844 http://zaguan.unizar.es/record/136211/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:136211 articulos driver 2026-02-17-20:40:47 ARTICLE