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

DOI10.1016/J.GEOMPHYS.2024.105264MaRDI QIDQ6596133

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

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)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Holomorphic quantization of linear field theory in the general boundary formulation
• Affine holomorphic quantization
• Star-product approach to quantum field theory: The free scalar field
• Stochastic partial differential equations. A modeling, white noise functional approach
• Locality and the structure of particle states
• White noise calculus and Fock space
• The Schrödinger wave functional and vacuum states in curved spacetime. II: Boundaries and foliations
• The Schrödinger wave functional and vacuum states in curved spacetime
• Generalized functionals in Gaussian spaces: The characterization theorem revisited
• Schrödinger and Fock representation for a field theory on curved spacetime
• On a dual pair of spaces of smooth and generalized random variables
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• A \(\mathrm{C}^*\)-algebraic approach to interacting quantum field theories
• Advances in algebraic quantum field theory
• Fields, observables and gauge transformations. I
• Fields, observables and gauge transformations. II
• The Schrödinger representation and its relation to the holomorphic representation in linear and affine field theory
• Geometry in a Fréchet Context
• Analysis, Geometry, and Modeling in Finance
• An Algebraic Approach to Quantum Field Theory
• Geometrization of quantum mechanics
• Malliavin Calculus for Lévy Processes with Applications to Finance
• Hybrid geometrodynamics: a Hamiltonian description of classical gravity coupled to quantum matter
• Geometric flavours of quantum field theory on a Cauchy hypersurface. II: Methods of quantization and evolution

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