000136211 001__ 136211
000136211 005__ 20240719195438.0
000136211 0247_ $$2doi$$a10.1016/j.geomphys.2024.105264
000136211 0248_ $$2sideral$$a139100
000136211 037__ $$aART-2024-139100
000136211 041__ $$aeng
000136211 100__ $$0(orcid)0000-0003-0694-155X$$aAlonso, José Luis$$uUniversidad de Zaragoza
000136211 245__ $$aGeometric flavors of Quantum Field theory on a Cauchy hypersurface. Part I: Gaussian analysis and other mathematical aspects
000136211 260__ $$c2024
000136211 5060_ $$aAccess copy available to the general public$$fUnrestricted
000136211 5203_ $$aIn 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].
000136211 536__ $$9info:eu-repo/grantAgreement/ES/AEI/PID2021-123251NB-I00$$9info:eu-repo/grantAgreement/ES/DGA/E48-23R
000136211 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000136211 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000136211 700__ $$0(orcid)0000-0003-1697-5710$$aBouthelier-Madre, Carlos
000136211 700__ $$0(orcid)0000-0003-4721-7381$$aClemente-Gallardo, Jesús$$uUniversidad de Zaragoza
000136211 700__ $$0(orcid)0000-0002-6044-0337$$aMartínez-Crespo, David$$uUniversidad de Zaragoza
000136211 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica
000136211 773__ $$g203 (2024), 105264 [25 pp.]$$pJ. geom. phys.$$tJOURNAL OF GEOMETRY AND PHYSICS$$x0393-0440
000136211 8564_ $$s700617$$uhttps://zaguan.unizar.es/record/136211/files/texto_completo.pdf$$yVersión publicada
000136211 8564_ $$s1757844$$uhttps://zaguan.unizar.es/record/136211/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000136211 909CO $$ooai:zaguan.unizar.es:136211$$particulos$$pdriver
000136211 951__ $$a2024-07-19-18:29:24
000136211 980__ $$aARTICLE