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Mass renormalization for the \(\lambda\Phi^4\) Euclidean lattice field. (English) Zbl 0453.60097

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60G60 Random fields
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
81P20 Stochastic mechanics (including stochastic electrodynamics)
81T08 Constructive quantum field theory
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References:

[1] Simon, B., The \(P(φ)_2\) Euclidean (Quantum) Field Theory (1974), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J · Zbl 1175.81146
[2] Guerra, F.; Rosen, L.; Simon, B., The \(P(φ)_2\) Euclidean quantum field theory as classical statistical mechanics, Ann. of Math., 101, Nos. 1, 2, 111-259 (1975) · Zbl 1495.82015
[3] Nelson, E., Probability theory and Euclidean field theory, (Velo, G.; Wightman, A., Constructive Quantum Field Theory (1973), Springer-Verlag: Springer-Verlag Berlin), 94-124
[4] Frölich, J., Schwinger functions and their generating functionals, II, Advances in Math., 23, 119-180 (1977)
[5] Deo, C., A functional central limit theorem for stationary random fields, Ann. of Prob., 3, No. 4, 708-715 (1975) · Zbl 0333.60028
[6] Glimm, J.; Jaffe, A., Critical Problems in Quantum Fields, (presented at Int. Coll. on Math. Methods of Quantum Field Theory (June 1975), CNRS: CNRS Marseille) · Zbl 0191.27101
[7] Glimm, J.; Jaffe, A., \(φ_2^4\) quantum field model in the single-phase region: Differentiability of the mass and bounds on critical exponents, Phys. Rev. D, 10, No. 2, 536-539 (1974)
[8] \( \textsc{G. Baker}d\)J. Math. Phys.16; \( \textsc{G. Baker}d\)J. Math. Phys.16
[9] Glimm, J.; Jaffe, A.; Spencer, T., The particle structure of the weakly coupled \(P(φ)_2\) model, (Velo, G.; Wightman, A., Constructive Quantum Field Theory (1973), Springer-Verlag: Springer-Verlag Berlin), 132-242
[10] Ito, K.; McKean, H. P., Diffusion Processes and their Sample Paths (1965), Academic Press: Academic Press New York · Zbl 0127.09503
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