Probabilistic aspects of quantum field theory (Q1141429)

scientific article; zbMATH DE number 3682804

Language	Label	Description	Also known as
English	Probabilistic aspects of quantum field theory	scientific article; zbMATH DE number 3682804

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instance of

scholarly article

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title

Probabilistic aspects of quantum field theory (English)

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published in

Journal of Soviet Mathematics

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publication date

1980

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zbMATH Keywords

probabilistic aspects of quantum field theory

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Existence of Green's functions in the Euclidean domain for the $P(\varphi)_2$ theory

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Renormalized power of a generalized random field and equations for the Green's functions in the Euclidean domain

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Q5333998

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The Wightman axioms and the mass gap for strong interactions of exponential type in two-dimensional space-time

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Homogeneous random fields and statistical mechanics

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A proof of the unitarity of $S$-matrix in a nonlocal quantum field theory

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There are no scalar Lie fields in three or more dimensional space-time

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On the duality condition for a Hermitian scalar field

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Integral representations for Schwinger functionals and the moment problem over nuclear spaces

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Euclidean field theory. I: The moment problem

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There are no Goldstone bosons in two dimensions

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Euclidean Green's functions for Jaffe fields

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Constructive quantum field theory. The 1973 'Ettore Majorana' international school of mathematical physics

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Feynman's path integral. Definition without limiting procedure

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Feynman path integrals. I: Linear and affine techniques. II: The Feynman- Green function

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Q4090901

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Measures on Schwartz distribution space and applications to $P(\varphi)_2$ field theories

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A generalization of the classical moment problem on $^*$-algebras with applications to relativistic quantum theory. I

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Representations of the CCR in the $(\phi^ 4)_ 3$ model: Independence of space cutoff

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Q4775029

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Exponential representations of the canonical commutation relations

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Gauge transformations and normal states of the CCR

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Commutators and self-adjointness of Hamiltonian operators

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On the Absence of Bound States in the λϕ<sub>2</sub><sup>4</sup> Quantum Field Model Without Symmetry Breaking

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Asymptotic Estimates of Feynman Integrals

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Q4114358

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On the equivalence of the Euclidean and Wightman formulation of field theory

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Boson fields with nonlinear selfinteraction in two dimensions

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Yukawa coupling of quantum fields in two dimensions. I

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The Yukawa coupling of quantum fields in two dimensions. II

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Boson fields with the $:\Phi^ 4:$ interaction in three dimensions

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Self-adjointness of the Yukawa$_{2}$ Hamiltonian

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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

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The $\lambda (\varphi^ 4)_ 2$ quantum field theory without cutoffs. II: The field operators and the approximate vacuum

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Infinite Renormalization of the Hamiltonian Is Necessary

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Singular perturbations of selfadjoint operators

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Positivity and self adjointness of the $P(\phi)_ 2$ Hamiltonian

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Rigorous quantum field theory models

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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>

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Phase transitions for $\phi_2^4$ quantum fields

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Matrix moment methods in perturbation theory, boson quantum field models, and anharmonic oscillators

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Existence and uniqueness of physical ground states

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The pressure is independent of the boundary conditions for $P\left( \phi \right)_2$ field theories

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An elementary proof of Dyson's power counting theorem

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Extremal decomposition of Wightman functions and of states on nuclear $^*$-algebras by Choquet theory

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From Euclidean to relativistic fields and on the notion of Markoff fields

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Prime field decompositions and infinitely divisible states on Borcher's tensor algebra

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A canonical structure for classical field theories

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Singular perturbations of positivity preserving semigroups via path space techniques

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The $:\phi^{2}:$ field in the $P(\phi)_{2}$ model

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The significance of conformal inversion in quantum field theory

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Holomorphic versions of the Fabrey-Glimm representations of the canonical commutation relations

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Convergence theorems for renormalized Feynman integrals with zero-mass propagators

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Distributional limits of renormalized Feynman integrals with zero-mass denominators

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Approximate vacuums in $( : \phi^{2m} : g(x))_ 2$ field theories and perturbation series

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Martin-Dynkin boundaries of random fields

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Hyperfunction quantum field theory

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Quantum field theory and the coloring problem of graphs

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Construction of quantum fields from Markoff fields

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The free Markoff field

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Time-ordered operator products of sharp-time quadratic forms

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The construction of stationary two-dimensional Markoff fields with an application to quantum field theory

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Some aspects of Markov and Euclidean field theories

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An application of modular Hilbert algebras: Duality for free Bose fields

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Q4102329

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Axioms for Euclidean Green's functions

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Axioms for Euclidean Green's functions. II

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Integrable Hamiltonian systems and interactions through quadratic constraints

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Support properties of the free measure for boson fields

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Q5653193

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Q4066072

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The (φ 2n ) 2 Field Hamiltonian for Complex Coupling Constant

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On the euclidean version of Haag's theorem in $P (\varphi )_2$ theories

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Markov structures on Clifford algebras

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Essential self-adjointness of Schrödinger operators with positive potentials

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Ergodic semigroups of positivity preserving self-adjoint operators

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Q4166017

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Distributions and Their Hermite Expansions

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Correlation inequalities and the mass gap in $P(\phi)_2$. I: Domination by the two point function

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Hypercontra ctive semigroups and two dimensional self-coupled Bose fields

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High-Energy Behavior in Quantum Field Theory

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The free fermion field as a Markov field

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Operator product expansions and composite field operators in the general framework of quantum field theory

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The connection between an Euclidean Gauss Markov vector field and the Real Proca Wightman field

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Convergence of Bogoliubov's method of renormalization in momentum space

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Identifiers

zbMATH Open document ID

0437.60079

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DOI

10.1007/BF01673628

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:1141429