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We give a direct construction of invariant measures and global flows for the stochastic quantization equation to the quantum field theoretical $\Phi ^4_3$-model on the $3$-dimensional torus.
The general theory of quantized fields
R. Jost · 1965
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Boson fields with the : Φ 4 : :\Phi^{4}: interaction in three dimensions
J. Glimm · 1968
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Methods of modern mathematical physics. I. Functional analysis
M. Reed and B. Simon · 1972
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Positivity of the ϕ 3 4 \phi^{4}_{3} Hamiltonian
J. Glimm and A. Jaffe · 1973
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The free Markoff field
E. Nelson · 1973
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Probability theory and euclidean field theory
E. Nelson · 1973
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The Wightman axioms and the mass gap for strong interactions of exponential type in two-dimensional space-time
S. Albeverio and R. Høegh-Krohn · 1974
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The λ φ 3 4 \lambda\varphi^{4}_{3} field theory in a finite volume
J. Feldman · 1974
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Verification of axioms for Euclidean and relativistic fields and Haag’s theorem in a class of P ( φ ) 2 P(\varphi)_{2} -models
J. Fröhlich · 1974
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The P ( ϕ ) 2 P(\phi)_{2} Euclidean (quantum) field theory
B. Simon · 1974
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Oscillateur anharmonique mesures quasi-invariantes sur C ( 𝐑 , 𝐑 ) C({\bf R},\ {\bf R}) et théorie quantique des champs en dimension d = 1 d=1
P. Courrège and P. Renouard · 1975
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The 𝐏 ( ϕ ) 2 {\bf P}(\phi)_{2} Euclidean quantum field theory as classical statistical mechanics. I, II
F. Guerra, L. Rosen and B. Simon · 1975
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The λ ϕ 3 4 \lambda\phi^{4}_{3} Euclidean quantum field theory in a periodic box
Y. M. Park · 1975
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Processus de diffusion à valeurs dans 𝐑 {\bf R} et mesures quasi-invariantes sur C ( 𝐑 , 𝐑 ) C({\bf R},\ {\bf R})
P. Priouret and M. Yor · 1975
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Methods of modern mathematical physics. II. Fourier analysis, self-adjointness
M. Reed and B. Simon · 1975
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The Wightman axioms and the mass gap for weakly coupled ( Φ 4 ) 3 (\Phi^{4})_{3} quantum field theories
J. S. Feldman and K. Osterwalder · 1976
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Infrared bounds, phase transitions and continuous symmetry breaking
J. Fröhlich, B. Simon and T. Spencer · 1976
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Boundary conditions for the P ( ϕ ) 2 P(\phi)_{2} Euclidean field theory
F. Guerra, L. Rosen and B. Simon · 1976
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The infinite volume limit of the ϕ 3 4 \phi^{4}_{3} model
J. Magnen and R. Sénéor · 1976
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Nelson’s symmetry and all that in the Yukawa2 and ( ϕ 4 ) 3 (\phi^{4})_{3} field theories
E. Seiler and B. Simon · 1976
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Convergence of lattice approximations and infinite volume limit in the ( λ ϕ 4 − σ ϕ 2 − τ ϕ ) 3 (\lambda\phi^{4}-\sigma\phi^{2}-\tau\phi)_{3} field theory
Y. M. Park · 1977
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Methods of modern mathematical physics. IV. Analysis of operators
M. Reed and B. Simon · 1978
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Invariant wave equations
G. Velo and A. S. Wightman, editors · 1978
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Some results for the exponential interaction in two or more dimensions
S. Albeverio, G. Gallavotti, and R. Høegh-Krohn · 1979
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Methods of modern mathematical physics. III
M. Reed and B. Simon · 1979
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Ultraviolet stability in Euclidean scalar field theories
G. Benfatto, M. Cassandro, G. Gallavotti, F. Nicolò, E. Olivieri, E. Presutti and E. Scacciatelli · 1980
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Collected papers. Vol. 2
J. Glimm and A. Jaffe · 1980
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Quantum physics
J. Glimm and A. Jaffe · 1981
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Perturbation theory without gauge fixing
G. Parisi and Y. S. Wu · 1981
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Euclidean quantum mechanics and stochastic integrals
R. F. Streater · 1981
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An alternate constructive approach to the φ 3 4 \varphi^{4}_{3} quantum field theory, and a possible destructive approach to φ 4 4 \varphi^{4}_{4}
A. D. Sokal · 1982
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A new proof of the existence and nontriviality of the continuum φ 2 4 \varphi^{4}_{2} and φ 3 4 \varphi^{4}_{3} quantum field theories
D. C. Brydges, J. Fröhlich and A. D. Sokal · 1983
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Skeleton inequalities and the asymptotic nature of perturbation theory for Φ 4 \Phi^{4} -theories in two and three dimensions
A. Bovier and G. Felder · 1984
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Collected papers. Vol. 1: Quantum Field Theory and Statistical Mechanics
J. Glimm and A. Jaffe · 1985
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On the stochastic quantization of field theory
G. Jona-Lasinio and P. K. Mitter · 1985
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Nonstandard methods in stochastic analysis and mathematical physics
S. Albeverio, R. Høegh-Krohn, J. E. Fenstad, and T. Lindstrøm · 1986
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Construction and Borel summability of infrared Φ 4 4 \Phi^{4}_{4} by a phase space expansion
J. Feldman, J. Magnen, V. Rivasseau and R. Sénéor · 1987
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An infinite-dimensional stochastic differential equation with state space C ( 𝐑 ) C({\bf R})
A remark on the nonequivalence of the time-zero ϕ 3 4 \phi^{4}_{3} -measure with the free field measure
S. Albeverio and S. Liang · 2008
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Ramification of rough paths
M. Gubinelli · 2010
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Fourier analysis and nonlinear partial differential equations
H. Bahouri, J.-Y. Chemin, and R. Danchin · 2011
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Quantum mechanics and quantum field theory
J. Dimock · 2011
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Normal approximations with Malliavin calculus
I. Nourdin and G. Peccati · 2012
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Variational methods in nonlinear field equations
V. Benci and D. Fortunato · 2014
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K. Iwata · 1987
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Topics in Fourier analysis and function spaces
H.-J. Schmeisser and H. Triebel · 1987
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Stochastic quantization of field theory in finite and infinite volume
V. S. Borkar, R. T. Chari, and S. K. Mitter · 1988
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Stochastic differential equations and diffusion processes
N. Ikeda and S. Watanabe · 1989
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General Principles of Quantum Field Theory
N. N. Bogolubov, A. A. Logunov, A. I. Oksak and I. Todorov · 1990
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Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms
S. Albeverio and M. Röckner · 1991
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S. K. Mitter · 1991
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Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions d ⩽ 3 d\leqslant 3
J. Fröhlich, A. Knowles, B. Schlein and V. Sohinger · 2017
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Convergence of the two-dimensional dynamic Ising-Kac model to Φ 2 4 \Phi^{4}_{2}
J.-C. Mourrat and H. Weber · 2017
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The dynamic Φ 3 4 {\Phi}_{3}^{4} model comes down from infinity
J.-C. Mourrat and H. Weber · 2017
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Global well-posedness of the dynamic Φ 4 \Phi^{4} model in the plane
J.-C. Mourrat and H. Weber · 2017
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Construction of ϕ 3 4 \phi^{4}_{3} diagrams for pedestrians
J.-C. Mourrat, H. Weber and W. Xu · 2017
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Restricted Markov uniqueness for the stochastic quantization of P ( Φ ) 2 P(\Phi)_{2} and its applications
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Paracontrolled distributions and the 3-dimensional stochastic quantization equation
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Discretisations of rough stochastic PDEs
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The strong Feller property for singular stochastic PDEs
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Tightness of the Ising–Kac model on the two-dimensional torus
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Multiplicative stochastic heat equations on the whole space
M. Hairer and C. Labbé · 2018
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Large-scale behavior of three-dimensional continuous phase coexistence models
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Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits
M. Lewin, P. T. Nam, and N. Rougerie · 2018
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Lattice approximation to the dynamical Φ 3 4 \Phi_{3}^{4} model
R. Zhu and X. Zhu · 2018
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Dirichlet form associated with the Φ 3 4 \Phi^{4}_{3} model
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Weak universality for a class of 3d stochastic reaction-diffusion models
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