Boundary conditions for the P(φ) 2 euclidean field theory
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 25 (1976) no. 3, pp. 231-334.
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Guerra, Francesco; Rosen, Lon; Simon, Barry. Boundary conditions for the $P(\phi )_2$ euclidean field theory. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 25 (1976) no. 3, pp. 231-334. http://www.numdam.org/item/AIHPA_1976__25_3_231_0/

[1] N. Abramowitz and I. Stegun, Handbook of Mathematical Functions, U. S. Govt. Printing Office, 1964.

[2] R. Baumel, Princeton University Thesis, in preparation.

[3] P. Cartier, Séminaire Bourbaki Lecture, to appear.

[4] S. Coleman, Quantum Sine-Gordon Equation as the Massive Thirring Model, Phys. Rev. D, t. 11, p. 2088-2097.

[5] P. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience, New York, 1953. | Zbl

[6] J. Dimock, Asymptotic Perturbation Expansions in the P(φ)2 Quantum Field Theory, Commun. Math. Phys., t. 35, 1974, p. 347-356. | MR

[7] J. Dimock and J. Glimm, Measures on Schwartz Distribution Space and Applications to P(φ)2 Field Theories, Adv. in Math., t. 12, 1974, p. 58-83. | MR | Zbl

[8] R.L. Dobrushin and R.A. Minlos, Construction of a One-Dimensional Quantum Field via a Continuous Markov Field, Func. Anal. and Applic., t. 7, 1973, p. 324-325. | Zbl

[9] J. Eachus and L. Streit, Exact Solution of the Quadratic Interaction Hamiltonian, Reports on Math. Phys., t. 4, 1973, p. 161-182. | MR

[10] M. Fisher and J. Lebowitz, Asymptotic Free Energy of a System with Periodic Boundary Conditions, Commun. Math. Phys., t. 19, 1970, p. 251-272. | MR

[11] J. Fröhlich, Schwinger Functions and their Generating Functionals, I, Helv. Phys. Acta., t. 47, 1974, p. 265 ; II, Adv. Math., to appear. | MR | Zbl

[12] J. Fröhlich, preprint in preparation.

[13] I.M. Gelfand and A.M. Vilenkin,Generalized Functions , Vol. 4 : Applications of Harmonic Analysis, Academic Press, New York, 1964. | MR

[14] J. Ginibre, General Formulation of Griffiths' Inequalities, Commun. Math. Phys., t. 16, 1970, p. 310-328. | MR

[15] J. Ginibre, Some Applications of Functional Integration in Statistical Mechanics, in Statistical Mechanics and Quantum Field Theory, ed. C. Dewitt and R. Stora, Gordon and Breach, New York, 1971.

[16] J. Glimm, Boson Fields with Non-linear Self-Interaction in Two Dimensions, Commun. Math. Phys., t. 8, 1968, p. 12-25. | MR | Zbl

[17] J. Glimm and A. Jaffe, The λ(φ4)2 Quantum Field Theory without Cutoffs, II. The Field Operators and the Approximate Vacuum, Ann. Math., t. 91, 1970, p. 362-401. | MR | Zbl

[18] J. Glimm and A. Jaffe, Quantum Field Theory Models, in Statistical Mechanics and Quantum Field Theory, ed. C. Dewitt and R. Stora, Gordon and Breach, New York, 1971.

[19] J. Glimm and A. Jaffe, The λ(φ4)2 Quantum Field Theory without Cutoffs, IV. Perturbations of the Hamiltonian, J. Math. Phys., t. 13, 1972, p. 1568-1584. | MR

[20] J. Glimm and A. Jaffe, Positivity and Self-Adjointness of the P(φ)2 Hamiltonian, Commun. Math. Phys., t. 22, 1971, p. 253-258. | MR | Zbl

[21] J. Glimm and A. Jaffe, Positivity of the (φ4)3 Hamiltonian, Fort. der-Physik, t. 21, 1973, p. 327-376. | MR

[22] J. Glimm and A. Jaffe, φ42 Quantum Field Model in the Single-Phase Region: Differentiability of the Mass and Bounds on Critical Exponents, Phys. Rev., D 10, 1974, p. 536-539.

[23] J. Glimm, A. Jaffe and T. Spencer, The particle Structure of the Weakly Coupled P(φ)2 Model and Other Applications of High Temperature Expansions, II. The Cluster Expansion, in Constructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer-Verlag, Berlin, 1973. | MR

[24] J. Glimm, A. Jaffe and T. Spencer, The Wightman Axioms and Particle Structure in the P(φ)2 Quantum Field Model, Ann. Math., t. 100, 1974, p. 585-632. | MR

[25] F. Guerra, Uniqueness of the Vacuum Energy Density and Van Hove Phenomena in the Infinite Volume Limit for Two Dimensional Self-Coupled Bose Fields. Phys. Rev. Lett., t. 28, 1972, 1213.

[26] F. Guerra, Bose Field Theory as Classical Statistical Mechanics, I. The Variational Principle and Equilibrium Equations, in Constructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer-Verlag, Berlin, 1973. | MR

[27] F. Guerra, L. Rosen and B. Simon, Nelson's Symmetry and the Infinite Volume Behavior of the Vacuum in P(φ)2, Commun. Math. Phys., t. 27, 1972, p. 10-22. | MR

[28] F. Guerra, L. Rosen and B. Simon, The Vacuum Energy for P(φ)2. Infinite Volume Limit and Coupling Constant Dependence, Commun. Math. Phys., t. 29, 1973, p. 233-247. | MR

[29] F. Guerra, L. Rosen and B. Simon, The P(φ)2 Euclidean Quantum Field Theory, Ann. Math., t. 101, 1975, p. 111-259. | MR

[30] F. Guerra, L. Rosen and B. Simon, Correlation Inequalities and the Mass Gap in P(φ)2, III. The Mass Gap for a Class of Strongly Coupled Theories with Nonzero External Field, Commun. Math. Phys., t. 41, 1975, p. 19-32. | MR

[31] T. Hida, Stationary Stochastic Processes, Princeton University Press, 1970. | MR | Zbl

[32] R. Höegh-Krohn, Relativistic Quantum Statistical Mechanics in Two-Dimensional Space-Time, Commun. Math. Phys., t. 38, 1974, p. 195-224. | MR

[33] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966. | MR | Zbl

[34] A. Klein, Quadratic Expressions in a Free Boson Field, Trans. Amer. Math. Soc., t. 181, 1973, p. 439-456. | MR | Zbl

[35] J. Lebowitz, GHS and Other Inequalities, Commun. Math. Phys., t. 35, 1974, p. 87-92. | MR

[36] J. Lebowitz and A. Martin-Löf, On the Uniqueness of the Equilibrium State for Ising Spin Systems, Commun. Math. Phys., t. 25, 1972, p. 276-282. | MR

[37] J. Lebowitz and O. Penrose, Decay of Correlations, Phys. Rev. Lett., t. 31, 1973, p. 749-752.

[38] A. Lenard and C. Newman, Infinite Volume Asymptotics in P(φ)2 Field Theory, Commun. Math. Phys., t. 39, 1974, p. 243-250. | MR

[39] A.J. Lions, Lectures on Elliptic Partial Differential Equations, Tata Institute, 1967. | MR | Zbl

[40] E. Nelson, Feynman Integrals and the Schrödinger Equation, J. Math. Phys., t. 5, 1964, p. 332-343. | MR | Zbl

[41] E. Nelson, A Quartic Interaction in Two Dimensions, in Mathematical Theory of Elementary Particles, ed. R. Goodman and I. Segal, M. I. T. Press, Cambridge, Mass. 1966. | MR

[42] E. Nelson, Quantum Fields and Markoff Fields, in Partial Differential Equations, Ed. D. Spencer, A. M. S., Providence, 1973. | MR | Zbl

[43] E. Nelson, The Free Markoff Field, J. Func. Anal., t. 12, 1973, p. 211-227. | MR | Zbl

[44] E. Nelson, Probability Theory and Euclidean Field Theory, in Constructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer-Verlag, 1973. | MR | Zbl

[45] C. Newman, Gaussian Correlation Inequalities for FerromagnetsZ. Wahrscheinlichkeitstheorie verw. Gebiete , , t. 33, 1975, p. 75-93. | MR | Zbl

[46] I.D. Novikov, Independence of Free Energy with Respect to Boundary Conditions, Func. Anal. Applic., t. 3, 1969, p. 71-84. (English trans., p. 58-67). | MR | Zbl

[47] K. Osterwalder and R. Schrader, On the Uniqueness of the Energy Density in the Infinite Volume Limit for Quantum Fields Models, Helv. Phys. Acta., t. 45, 1972, p. 746-754. | MR

[48] J. Percus, Correlation Inequalities for Ising Spin Systems, Commun. Math. Phys., t. 40, 1975, p. 283-308. | MR

[49] L. Pitner and L. Streit, Model Calculation of the Vacuum Energy Density for a Self-Coupled Bose Field, Acta Phys. Aust., t. 38, 1973, p. 361-366.

[50] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. I. Functional Analysis, Academic Press, New York, 1972. | Zbl

[51] D. Robinson, The Thermodynamic Pressure in Quantum Statistical Mechanics, Springer-Verlag, Berlin, 1971. | MR

[52] L. Rosen, Renormalization of the Hilbert Space in the Mass Shift Model, J. Math. Phys., t. 13, 1972, p. 918-927. | MR

[53] L. Rosen, Bose Field Theory as Classical Statistical Mechanics, II. The Lattice Approximation and Correlation Inequalities, in Constructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer-Verlag, 1973.

[54] D. Ruelle, Statistical Mechanics, Benjamin, New York, 1969. | MR | Zbl

[55] D. Ruelle, On the Use of « Small External Fields » in the Problem of Symmetry Breakdown in Statistical Mechanics, Ann. Phys., t. 69, 1972, p. 364-374.

[56] I. Segal, Tensor Algebras over Hilbert Spaces, ITrans. Amer. Math. Soc., t. 81, 1956, p. 106-134. | MR | Zbl

[57] I. Segal, Foundation of the Theory of Dynamical Systems of Infinitely Many Degrees of Freedom, I. Mat. Fys. Medd. Dansk. Vid. Selsk., t. 31, No. 12, 1959 ; II. Can. J. Math., t. 13, 1961, p. 1-18. | MR | Zbl

[58] I. Segal, Non-linear Functions of Weak Processes, I. J. Func. Anal., t. 4, 1969, p. 404- 451. | Zbl

[59] I. Segal, Construction of Non-linear Local Quantum Processes, I. Ann. Math., t. 92, 1970, p. 462-481. | MR | Zbl

[60] D. Shale, Linear Symmetries of the Free Boson Field, Trans. Amer. Math. Soc., t. 103, 1962, p. 149-167. | MR | Zbl

[61] B. Simon, On the Glimm-Jaffe Linear Lower Bound in P(φ)2 Field Theories J. Func. Anal., t. 10, 1972, p. 251-258. | MR

[62] B. Simon, The P(φ)2 Euclidean (Quantum) Field Theory, Princeton Univ. Press, 1974. | MR

[63] B. Simon and R. Griffiths, The (φ4)2 Field Theory as a Classical Ising Model, Commun. Math. Phys., t. 33, 1973, p. 145-164. | MR

[64] B. Simon and R. Höegh-Krohn, Hypercontractive Semigroups and Two-Dimensional Self-Coupled Bose Fields, J. Func. Anal., t. 9, 1972, p. 121-180. | MR | Zbl

[65] P. Sodano, Thesis, University of Naples, 1974 (unpubl.).

[66] T. Spencer, The Mass Gap for the P(φ)2 Quantum Field Model with a Strong External Field, Commun. Math. Phys., t. 39, 1974, p. 63-76. | MR

[67] G. Sylvester, Representations and Inequalities for Ising Model Ursell Functions, Commun. Math. Phys., t. 42, 1975, p. 209-220. | MR