Along Paths Inspired by Ludwig Streit: Stochastic Equations for Quantum Fields and Related Systems

DOI10.1007/978-3-319-07245-6_1zbMath1498.60279OpenAlexW2475700294MaRDI QIDQ5038272

Sergio A. Albeverio

Publication date: 30 September 2022

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-07245-6_1

zbMATH Keywords

stochastic partial differential equationsquantum field theorystochastic quantizationFeynman path integralsfunctional integrationinfinite dimensional integrals

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) White noise theory (60H40) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items

Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus, Non-local Markovian symmetric forms on infinite dimensional spaces. II: Applications: non local stochastic quantization of space cut-off quantum fields and infinite particle systems, Non-local Markovian symmetric forms on infinite dimensional spaces. I: The closability and quasi-regularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A theory of regularity structures
• Nonlinear parabolic stochastic differential equations with additive colored noise on \({\mathbb{R}}^ d\times {\mathbb{R}}_ +:\) A regulated stochastic quantization
• Dirichlet forms and symmetric Markov processes.
• Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions
• Small noise asymptotic expansions for stochastic PDE's. I: The case of a dissipative polynomially bounded non linearity
• Essential self-adjointness of Dirichlet operators on a path space with Gibbs measures via an SPDE approach
• The statistical mechanics of quantum lattice systems. A path integral approach.
• Generalized Brownian functionals and the Feynman integral
• An infinite dimensional stochastic differential equation with state space C(\({\mathbb{R}})\)
• On the stochastic quantization of field theory
• Convergence of Dirichlet forms and associated Schrödinger operators
• Stochastic multiplicative measures, generalized Markov semigroups, and group-valued stochastic processes and fields
• Traces of harmonic functions and a new path space for the free quantum field
• Stochastic quantization of field theory in finite and infinite volume
• Dirichlet forms and white noise analysis
• Classical Dirichlet forms on topological vector spaces - the construction of the associated diffusion process
• Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions
• Some results for the exponential interaction in two or more dimensions
• Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I
• Capacity and quantum mechanical tunneling
• A characterization of Hida distributions
• Uniqueness of generalized Schrödinger operators and applications
• Dirichlet forms and analysis on Wiener space
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Invariant states on random and quantum fields: \(\phi\)-bounds and white noise analysis
• Homogeneous random fields and statistical mechanics
• Intersection local times of independent Brownian motions as generalized white noise functionals
• Intersection local times as generalized white noise functionals
• Models of local relativistic quantum fields with indefinite metric (in all dimensions)
• A mathematical construction of the non-Abelian Chern-Simons functional integral
• Exponential integrability and application to stochastic quantization
• A Markov property for Gaussian processes with a multidimensional parameter
• Infinite-dimensional stochastic differential equations obtained by subordination and related Dirichlet forms.
• Strong solutions to the stochastic quantization equations.
• Complex Dirichlet forms: Non symmetric diffusion processes and Schrödinger operators
• Selfadjointness of some infinite-dimensional elliptic operators and application to stochastic quantization
• Generalized functionals in Gaussian spaces: The characterization theorem revisited
• The Wightman axioms and the mass gap for strong interactions of exponential type in two-dimensional space-time
• Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators
• The \(P(\phi)_2\) Euclidean quantum field theory as classical statistical mechanics. I.
• The free Markoff field
• Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms
• Invariant measures for SDEs driven by Lévy noise: a case study for dissipative nonlinear drift in infinite dimension
• Hyperfinite Dirichlet forms and stochastic processes
• Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size
• Mathematical theory of Feynman path integrals. An introduction
• Quasi regular Dirichlet forms and the stochastic quantization problem
• Markov processes and generalized Schrödinger equations
• Some Methods of Infinite Dimensional Analysis in Hydrodynamics: An Introduction
• FUNCTIONAL-INTEGRAL SOLUTION FOR THE SCHRÖDINGER EQUATION WITH POLYNOMIAL POTENTIAL: A WHITE NOISE APPROACH
• DIRICHLET FORMS IN TERMS OF WHITE NOISE ANALYSIS I: CONSTRUCTION AND QFT EXAMPLES
• DIRICHLET FORMS IN TERMS OF WHITE NOISE ANALYSIS II: CLOSABILITY AND DIFFUSION PROCESSES
• ANALYSIS OF THE STOCHASTIC FITZHUGH–NAGUMO SYSTEM
• Feynman integrals as Hida distributions: the case of non-perturbative potentials
• Regularization of Hamiltonians and processes
• The Feynman integrand as a Hida distribution
• Logarithmic Sobolev Inequalities
• Dirichlet forms and diffusion processes on rigged Hilbert spaces
• Energy forms, Hamiltonians, and distorted Brownian paths
• On quantum theory in terms of white noise
• Construction of relativistic quantum fields in the framework of white noise analysis
• The complex scaled Feynman–Kac formula for singular initial distributions
• CHERN–SIMONS THEORY, HIDA DISTRIBUTIONS, AND STATE MODELS
• A RIGOROUS CONSTRUCTION OF ABELIAN CHERN-SIMONS PATH INTEGRALS USING WHITE NOISE ANALYSIS
• Polymer measure: Varadhan's renormalization revisited
• SYSTEMS OF CLASSICAL PARTICLES IN THE GRAND CANONICAL ENSEMBLE, SCALING LIMITS AND QUANTUM FIELD THEORY
• Subordination of symmetric quasi -regular Dirichlet forms
• REMARK ON THE INTEGRATION BY PARTS FORMULA FOR THE $\phi_3^4$-QUANTUM FIELD MODEL
• Metastability
• A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise