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We present a new construction of the Euclidean $\Phi^4$ quantum field theory on $\mathbb{R}^3$ based on PDE arguments.
A modified model of Euclidean quantum field theory
K. Symanzik · 1964
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Derivation of the Schrödinger equation from Newtonian mechanics
E. Nelson · 1966
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Dynamical theories of Brownian motion
E. Nelson · 1967
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Boson fields with the : ϕ 4 : :\phi^{4}: interaction in three dimensions
J. Glimm · 1968
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Positivity of the ϕ 3 4 \phi^{4}_{3} Hamiltonian
J. Glimm and A. Jaffe · 1973
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Axioms for Euclidean Green’s functions
K. Osterwalder and R. Schrader · 1973
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Constructive quantum field theory
G. Velo and A. Wightman, editors · 1973
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B. Simon · 1974
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Axioms for Euclidean Green’s functions II
K. Osterwalder and R. Schrader · 1975
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The Wightman axioms and the mass gap for weakly coupled ϕ 3 4 \phi^{4}_{3} quantum field theories
J. S. Feldman and K. Osterwalder · 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 Y u k a w a 2 {Yukawa}_{2} and ( ϕ 4 ) 3 (\phi^{4})_{3} field theories
E. Seiler and B. Simon · 1976
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Hilbert’s sixth problem: mathematical treatment of the axioms of physics
A. S. Wightman · 1976
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The relativistic field equation of the λ ϕ 3 4 \lambda\phi^{4}_{3} quantum field theory
J. S. Feldman and R. Ra̧czka · 1977
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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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Some probabilistic techniques in field theory
G. Benfatto, M. Cassandro, G. Gallavotti, F. Nicolò, E. Olivieri, E. Presutti, and E. Scacciatelli · 1978
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Time-ordered products and Schwinger functions
J. P. Eckmann and H. Epstein · 1979
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Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
J.-M. Bony · 1981
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Remarques sur un théorème de J.-M. Bony
Y. Meyer · 1981
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Perturbation theory without gauge fixing
G. Parisi and Y. S. Wu · 1981
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Ultraviolet stability in field theory. The φ 3 4 \varphi_{3}^{4} model
T. Bałaban · 1983
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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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On the stochastic quantization of field theory
G. Jona-Lasinio and P. K. Mitter · 1985
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K. Gawędzki and A. Kupiainen · 1986
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J. Glimm and A. Jaffe · 1987
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An infinite dimensional stochastic differential equation with state space C(R)
K. Iwata · 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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Statistical mechanics of the nonlinear Schrödinger equation
J. L. Lebowitz, H. A. Rose, and E. R. Speer · 1988
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Statistical mechanics of the nonlinear Schrödinger equation. II. Mean field approximation
J. L. Lebowitz, H. A. Rose, and E. R. Speer · 1989
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Block spin approach to ϕ 3 4 \phi^{4}_{3} field theory
H. Watanabe · 1989
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Symmetric solutions of semilinear stochastic equations
J. Zabczyk · 1989
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Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms
S. Albeverio and M. Röckner · 1991
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From Perturbative to Constructive Renormalization
V. Rivasseau · 1991
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Introduction to algebraic and constructive quantum field theory
J. C. Baez, I. E. Segal, and Z.-F. Zhou · 1992
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Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory
R. Fernández, J. Fröhlich, and A. D. Sokal · 1992
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Periodic nonlinear Schrödinger equation and invariant measures
J. Bourgain · 1994
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The short distance behavior of ϕ 3 4 \phi^{4}_{3}
D. Brydges, J. Dimock, and T. R. Hurd · 1995
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Erratum: Statistical mechanics of nonlinear wave equations. iv. cubic schrödinger
H. P. McKean · 1995
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Statistical mechanics of nonlinear wave equations. iv. cubic schrödinger
H. P. McKean · 1995
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Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
J. Bourgain · 1996
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The renormalization group according to Balaban III. Convergence
J. Dimock · 2014
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A Course on Rough Paths: With an Introduction to Regularity Structures
P. K. Friz and M. Hairer · 2014
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A theory of regularity structures
M. Hairer · 2014
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On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on R d R^{d} , d ≥ 3 d\geq 3
Á. Bényi, T. Oh, and O. Pocovnicu · 2015
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Paracontrolled distributions and singular PDEs
M. Gubinelli, P. Imkeller, and N. Perkowski · 2015
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Regularity structures and the dynamical ϕ 3 4 \phi^{4}_{3} model
M. Hairer · 2015
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A Non-Gaussian Fixed Point for ϕ 4 \phi^{4} in 4 ? ε 4?\varepsilon Dimensions
D. Brydges, J. Dimock, and T. R. Hurd · 1998
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Differential equations driven by rough signals
T. Lyons · 1998
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Wavelets and Renormalization
G. Battle · 1999
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Compact embeddings of vector-valued sobolev and besov spaces
H. Amman · 2000
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Constructive quantum field theory
A. Jaffe · 2000
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H − C 1 H-C^{1} maps and elliptic SPDEs with polynomial and exponential perturbations of Nelson’s Euclidean free field
S. Albeverio and M. W. Yoshida · 2002
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Stochastic quantization, reflection positivity, and quantum fields
A. Jaffe · 2015
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Renormalization Group and Stochastic PDEs
A. Kupiainen · 2016
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Construction of ϕ 3 4 \phi^{4}_{3} diagrams for pedestrians
J.-C. Mourrat, H. Weber, and W. Xu · 2016
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Random data wave equations
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The invariant measure and the flow associated to the Φ 3 4 \Phi^{4}_{3} -quantum field model
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Statistical mechanics of lattice systems: a concrete mathematical introduction
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The dynamic Φ 3 4 \Phi^{4}_{3} 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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Global solutions to elliptic and parabolic Φ 4 \Phi^{4} models in Euclidean space
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Tightness of the Ising-Kac model on the two-dimensional torus
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Space-time localisation for the dynamic ϕ 3 4 \phi^{4}_{3} model
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Critical Exponents for Long-Range o ( n ) o(n) Models Below the Upper Critical Dimension
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