136137 20260217205516.0 doi 10.1016/j.geomphys.2024.105265 sideral 139126 ART-2024-139126 eng Alonso, José Luis Universidad de Zaragoza (orcid)0000-0003-0694-155X Geometric flavours of quantum field theory on a Cauchy hypersurface. Part II: Methods of quantization and evolution 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 second part we use the tools of Gaussian analysis in infinite dimensional spaces introduced in the first part to describe rigorously the procedures of geometric quantization in the space of Cauchy data of a scalar theory. This leads us to discuss and establish relations between different pictures of QFT. We also apply these tools to describe the geometrization of the space of pure states of quantum field theory as a Kähler manifold. We use this to derive an evolution equation that preserves the geometric structure and avoid norm losses in the evolution. This leads us to a modification of the Schrödinger equation via a quantum connection that we discuss and exemplify in a simple case info:eu-repo/grantAgreement/ES/AEI/PID2021-123251NB-I00 info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/grantAgreement/ES/MCIN/AEI/10.13039/501100011033 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), 41 pp. J. geom. phys. JOURNAL OF GEOMETRY AND PHYSICS 0393-0440 1001253 http://zaguan.unizar.es/record/136137/files/texto_completo.pdf Versión publicada 1780039 http://zaguan.unizar.es/record/136137/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:136137 articulos driver 2026-02-17-20:27:02 ARTICLE