Verification of axioms for euclidean and relativistic fields and Haag’s theorem in a class of P(ϕ) 2 -models
Fröhlich, Jürg
Annales de l'I.H.P. Physique théorique, Tome 21 (1974), p. 271-317 / Harvested from Numdam
Publié le : 1974-01-01
@article{AIHPA_1974__21_4_271_0,
     author = {Fr\"ohlich, J\"urg},
     title = {Verification of axioms for euclidean and relativistic fields and Haag's theorem in a class of $P(\varphi )\_2$-models},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {21},
     year = {1974},
     pages = {271-317},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1974__21_4_271_0}
}
Fröhlich, Jürg. Verification of axioms for euclidean and relativistic fields and Haag’s theorem in a class of $P(\varphi )_2$-models. Annales de l'I.H.P. Physique théorique, Tome 21 (1974) pp. 271-317. http://gdmltest.u-ga.fr/item/AIHPA_1974__21_4_271_0/

[1] H. Araki, J. Math. Phys., t. 1, 1960, p. 492. | MR 127821 | Zbl 0099.22906

[2] H. Araki, Comm. Math. Phys., t. 20, 1971, p. 9. | MR 290709 | Zbl 0203.57101

[3] P. Colella and O. Lanford, « Sample Field Behaviour for the Free Markov Random Field », in Constructive Quantum Field Theory, G. Velo and A. Wightman (eds.), Lecture Notes in Physics, Vol. 25, Springer Verlag, Berlin-Heidelberg-New York, 1974. | MR 395513 | Zbl 0346.28004

[4] J. Dimock, Asymptotic Perturbation Expansion in the P(ϕ)2 Quantum Field Theory, NYU Preprint, 1973. | MR 334756

[5] E.B. Dynkin, Markov Processes, Vol. I, II, Springer-Verlag, Berlin-Heidelberg- New York, 1965. | MR 193671 | Zbl 0132.37901

[6] J. Fröhlich, Schwinger Functions and Their Generating Functionals, I. Helv. Phys. Acta, t. 47, 1974, p. 265. | MR 436830 | Zbl 0345.46057

[7] J. Fröhlich, Schwinger Functions and Their Generating Functionals, II. Harvard Preprint, 1973, to appear in Adv. Math. | MR 436830 | Zbl 0345.46058

[8] J. Glimm, Comm. Math. Phys., t. 8, 1968, p. 12. | MR 231601 | Zbl 0173.29903

[9] J. Glimm and A. Jaffe, « Boson Quantum Field Models », in Mathematics of Contemporary Physics, ed. by R. Streater, Academic Press, New York-London, 1972. | MR 674511

[10] J. Glimm and A. Jaffe, J. Math. Phys., t. 13, 1972, p. 1568.

[11] J. Glimm and A. Jaffe, « The Entropy Principle for Vertex Functions in Quantum Field Models », to appear in Ann. Inst. « Henri Poincaré ». | Numdam | MR 391796

[12] J. Glimm, A. Jaffe, and T. Spencer, « The Wightman Axioms and Particle Structure in the P(ϕ)2 Quantum Field Model », to appear in Ann. Math.

[13] J. Glimm, A. Jaffe, and T. Spencer, « The Particle Structure of the Weakly Coupled P(ϕ)2 Models and Other Applications of High Temperature Expansions, Part II », in Constructive Quantum Field Theory, G. Velo and A. Wightman (eds.), Lecture Notes in Physics, Vol. 25, Springer-Verlag, Berlin-Heidelberg-New York, 1974. | MR 395513

[14] F. Guerra, Phys. Rev. Lett., t. 28, 1972, p. 1213.

[15] F. Guerra, L. Rosen, and B. Simon, Comm. Math. Phys., t. 27, 1972, p. 10 ; and t. 29, 1973, p. 233.

[16] F. Guerra, L. Rosen, and B. Simon, « The P(φ)2 Euclidean Quantum Field Theory as Classical Statistical Mechanics », to appear in Ann. Math.

[17] G. Hegerfeldt, From Euclidean to Relativistic Fields, University of Göttingen, Preprint, 1973.

[18] R. Jost, « The General Theory of Quantized Fields », Lectures in Applied Mathematics, American Math. Soc., Providence, 1965. | MR 177667 | Zbl 0127.19105

[19] J. Lew, Princeton Thesis, Princeton University, 1960.

[20] R. Minlos, Tr. Mosk. Mat. Obs., t. 8, 1959, p. 471.

[21] E. Nelson, A Quartic Interaction in Two Dimensions, ed. by R. Goodman and I. Segal, MIT Press, Cambridge, 1966. | MR 210416

[22] E. Nelson, J. Funct. Anal., t. 11, 1972, p. 211. | Zbl 0239.47012

[23] E. Nelson, « Quantum Fields and Markov Fields », in Proceedings of the Summer Institute on Partial Differential Equations, Berkeley, 1971, American Math. Soc., Providence, 1973. | MR 436832 | Zbl 0279.60096

[24] E. Nelson, J. Funct. Anal., t. 12, 1973, p. 97. | Zbl 0252.60053

[25] E. Nelson, J. Funct. Anal., t. 12, 1973, p. 211. | Zbl 0273.60079

[26] E. Nelson, « Probability Theory and Euclidean Field Theory », in Constructive Quantum Field Theory, G. Velo and A. Wightman (eds.), Lecture Notes in Physics, Vol. 25, Springer Verlag, Berlin-Heidelberg-New York, 1974. | MR 395513 | Zbl 0367.60108

[27] C. Newman, Zeros of the Partition Function for Generalized Ising Systems, NYU Preprint, 1973. | MR 484184

[28] K. Osterwalder and R. Schrader, « Euclidean Fermi Fields and a Feynman-Kac Formula for Boson-Fermion Models », to appear in Helv. Phys. Acta. | MR 366276

[29] K. Osterwalder and R. Schrader, Comm. Math. Phys., t. 31, 1973, p. 83. | MR 329492 | Zbl 0274.46047

[30] K. Osterwalder, « Euclidean Green's Functions and Wightman Distributions », in Constructive Quantum Field Theory, G. Velo and A. Wightman (eds.), Lecture Notes in Physics, Vol. 25, Springer-Verlag, Berlin-Heidelberg-New York, 1974. | Zbl 0335.46042

[31] K. Osterwalder and R. Schrader, to appear in Comm. Math. Phys. | MR 329492

[32] M. Reed, and L. Rosen, Support Properties of the Free Measure for Boson Fields, Princeton Preprint, 1973.

[33] D. Ruelle, Statistical Mechanics (Rigorous Results), W. A. Benjamin, New York- Amsterdam, 1969. | MR 289084 | Zbl 0177.57301

[34] R. Schrader, On the Euclidean Version of Haag's Theorem in P(ϕ)2 Theories, Freie Universität Berlin Preprint, 1973.

[35] B. Simon and R. Griffiths, Comm. Math. Phys., t. 33, 1973, p. 145. | MR 428998

[36] B. Simon, « Correlation Inequalities and the Mass Gap in P(ϕ)2, II. Uniqueness of the Vacuum for a Class of Strongly Coupled Theories », Ann. Math., to appear. | MR 373511

[37] B. Simon, « The P(ϕ)2 Euclidean (Quantum) Field Theory », to appear in Princeton Series in Physics, Princeton University Press, 1974. | MR 489552 | Zbl 1175.81146

[38] B. Simon, « Positivity of the Hamiltonian Semigroup and the Construction of Euclidean Region Fields », to appear in Helv. Phys. Acta. | MR 381541

[39] T. Spencer, The Mass Gap for the P(ϕ)2 Quantum Field Model with a Strong External Field, NYU Preprint, 1973. | MR 363294

[40] R. Streater and A. Wightman, PCT, Spin and Statistics and All That, W. A. Benjamin, New York-Amsterdam, 1964. | MR 161603 | Zbl 0135.44305

[41] K. Symanzik, « Euclidean Quantum Field Theory » in Local Quantum Theory, Proceedings of the International School of Physics, « Enrico Fermi », Course 45, ed. by R. Jost, Academic Press, New York-London, 1969.