Geometric flavours of quantum field theory on a Cauchy hypersurface. II: Methods of quantization and evolution

DOI10.1016/J.GEOMPHYS.2024.105265MaRDI QIDQ6596134

D. Martínez-Crespo, J. Clemente-Gallardo, J. Alonso, C. Bouthelier-Madre

Publication date: 2 September 2024

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

quantum field theoryHamiltonian representationsinfinite-dimensional Fourier transformquantum connectionsmodified Schrödinger equations

Mathematics Subject Classification ID

White noise theory (60H40) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Topological field theories in quantum mechanics (81T45) Applications of global differential geometry to the sciences (53C80) Topological quantum field theories (aspects of differential topology) (57R56) Stochastic calculus of variations and the Malliavin calculus (60H07) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) General theory of locally convex spaces (46A03) Locally convex Fréchet spaces and (DF)-spaces (46A04) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Geometric quantization (53D50) Distributions on infinite-dimensional spaces (46F25) Quantum state spaces, operational and probabilistic concepts (81P16)

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Geometric flavors of quantum field theory on a Cauchy hypersurface. I: Gaussian analysis and other mathematical aspects

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