Probabilistic aspects of quantum field theory

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Cites Work

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The $:\phi^{2}:$ field in the $P(\phi)_{2}$ model
Self-adjointness of the Yukawa$_{2}$ Hamiltonian
The construction of stationary two-dimensional Markoff fields with an application to quantum field theory
Euclidean Green's functions for Jaffe fields
On the equivalence of the Euclidean and Wightman formulation of field theory
Renormalized power of a generalized random field and equations for the Green's functions in the Euclidean domain
The connection between an Euclidean Gauss Markov vector field and the Real Proca Wightman field
Axioms for Euclidean Green's functions. II
Some aspects of Markov and Euclidean field theories
The significance of conformal inversion in quantum field theory
Integral representations for Schwinger functionals and the moment problem over nuclear spaces
Holomorphic versions of the Fabrey-Glimm representations of the canonical commutation relations
Measures on Schwartz distribution space and applications to $P(\varphi)_2$ field theories
Hyperfunction quantum field theory
Extremal decomposition of Wightman functions and of states on nuclear $^*$-algebras by Choquet theory
Prime field decompositions and infinitely divisible states on Borcher's tensor algebra
Euclidean field theory. I: The moment problem
There are no scalar Lie fields in three or more dimensional space-time
Existence of Green's functions in the Euclidean domain for the $P(\varphi)_2$ theory
Distributional limits of renormalized Feynman integrals with zero-mass denominators
Convergence theorems for renormalized Feynman integrals with zero-mass propagators
Matrix moment methods in perturbation theory, boson quantum field models, and anharmonic oscillators
Constructive quantum field theory. The 1973 'Ettore Majorana' international school of mathematical physics
Singular perturbations of positivity preserving semigroups via path space techniques
Markov structures on Clifford algebras
A canonical structure for classical field theories
A generalization of the classical moment problem on $^*$-algebras with applications to relativistic quantum theory. I
Martin-Dynkin boundaries of random fields
Homogeneous random fields and statistical mechanics
The free fermion field as a Markov field
Phase transitions for $\phi_2^4$ quantum fields
The Wightman axioms and the mass gap for strong interactions of exponential type in two-dimensional space-time
On the euclidean version of Haag's theorem in $P (\varphi )_2$ theories
Support properties of the free measure for boson fields
Feynman path integrals. I: Linear and affine techniques. II: The Feynman- Green function
Commutators and self-adjointness of Hamiltonian operators
Integrable Hamiltonian systems and interactions through quadratic constraints
The free Markoff field
Axioms for Euclidean Green's functions
From Euclidean to relativistic fields and on the notion of Markoff fields
There are no Goldstone bosons in two dimensions
Correlation inequalities and the mass gap in $P(\phi)_2$. I: Domination by the two point function
A proof of the unitarity of $S$-matrix in a nonlocal quantum field theory
Yukawa coupling of quantum fields in two dimensions. I
The Yukawa coupling of quantum fields in two dimensions. II
An elementary proof of Dyson's power counting theorem
Boson fields with nonlinear selfinteraction in two dimensions
Boson fields with the $:\Phi^ 4:$ interaction in three dimensions
The $\lambda (\varphi^ 4)_ 2$ quantum field theory without cutoffs. II: The field operators and the approximate vacuum
Convergence of Bogoliubov's method of renormalization in momentum space
Exponential representations of the canonical commutation relations
Positivity and self adjointness of the $P(\phi)_ 2$ Hamiltonian
Approximate vacuums in $( : \phi^{2m} : g(x))_ 2$ field theories and perturbation series
Representations of the CCR in the $(\phi^ 4)_ 3$ model: Independence of space cutoff
Essential self-adjointness of Schrödinger operators with positive potentials
Operator product expansions and composite field operators in the general framework of quantum field theory
Existence and uniqueness of physical ground states
Feynman's path integral. Definition without limiting procedure
Time-ordered operator products of sharp-time quadratic forms
Hypercontra ctive semigroups and two dimensional self-coupled Bose fields
Ergodic semigroups of positivity preserving self-adjoint operators
Construction of quantum fields from Markoff fields
Quantum field theory and the coloring problem of graphs
An application of modular Hilbert algebras: Duality for free Bose fields
High-Energy Behavior in Quantum Field Theory
Remark on the Existence of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>
The pressure is independent of the boundary conditions for $P\left( \phi \right)_2$ field theories
On the duality condition for a Hermitian scalar field
Gauge transformations and normal states of the CCR
On the Absence of Bound States in the λϕ₂⁴ Quantum Field Model Without Symmetry Breaking
Asymptotic Estimates of Feynman Integrals
Singular perturbations of selfadjoint operators
A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Quantum Field Theory without Cutoffs. I
Infinite Renormalization of the Hamiltonian Is Necessary
Rigorous quantum field theory models
Distributions and Their Hermite Expansions
The (φ 2n ) 2 Field Hamiltonian for Complex Coupling Constant

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