Boundary conditions for the $P{\left(\phi \right)}_2$ euclidean field theory

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1. [1] N. Abramowitz and I. Stegun, Handbook of Mathematical Functions, U. S. Govt. Printing Office, 1964. 
2. [2] R. Baumel, Princeton University Thesis, in preparation. 
3. [3] P. Cartier, Séminaire Bourbaki Lecture, to appear. 
4. [4] S. Coleman, Quantum Sine-Gordon Equation as the Massive Thirring Model, Phys. Rev. D, t. 11, p. 2088-2097. 
5. [5] P. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience, New York, 1953. Zbl0051.28802
6. [6] J. Dimock, Asymptotic Perturbation Expansions in the P(φ)2 Quantum Field Theory, Commun. Math. Phys., t. 35, 1974, p. 347-356. MR334756
7. [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. Zbl0313.28015MR349171
8. [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. Zbl0294.60081
9. [9] J. Eachus and L. Streit, Exact Solution of the Quadratic Interaction Hamiltonian, Reports on Math. Phys., t. 4, 1973, p. 161-182. MR356771
10. [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. MR278675
11. [11] J. Fröhlich, Schwinger Functions and their Generating Functionals, I, Helv. Phys. Acta., t. 47, 1974, p. 265 ; II, Adv. Math., to appear. Zbl0345.46057MR436830
12. [12] J. Fröhlich, preprint in preparation. 
13. [13] I.M. Gelfand and A.M. Vilenkin,Generalized Functions , Vol. 4 : Applications of Harmonic Analysis, Academic Press, New York, 1964. MR173945
14. [14] J. Ginibre, General Formulation of Griffiths' Inequalities, Commun. Math. Phys., t. 16, 1970, p. 310-328. MR269252
15. [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. [16] J. Glimm, Boson Fields with Non-linear Self-Interaction in Two Dimensions, Commun. Math. Phys., t. 8, 1968, p. 12-25. Zbl0173.29903MR231601
17. [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. Zbl0191.27005MR256677
18. [18] J. Glimm and A. Jaffe, Quantum Field Theory Models, inStatistical Mechanics and Quantum Field Theory, ed. C. Dewitt and R. Stora, Gordon and Breach, New York, 1971. Zbl0574.01019
19. [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. MR317683
20. [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. Zbl0221.47022MR353886
21. [21] J. Glimm and A. Jaffe, Positivity of the (φ4)3 Hamiltonian, Fort. der-Physik, t. 21, 1973, p. 327-376. MR408581
22. [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. [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, inConstructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer-Verlag, Berlin, 1973. MR395513
24. [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. MR363256
25. [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. [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. MR395513
27. [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. MR311242
28. [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. MR329501
29. [29] F. Guerra, L. Rosen and B. Simon, The P(φ)2 Euclidean Quantum Field Theory, Ann. Math., t. 101, 1975, p. 111-259. MR378670
30. [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. MR434230
31. [31] T. Hida, Stationary Stochastic Processes, Princeton University Press, 1970. Zbl0214.16401MR258106
32. [32] R. Höegh-Krohn, Relativistic Quantum Statistical Mechanics in Two-Dimensional Space-Time, Commun. Math. Phys., t. 38, 1974, p. 195-224. MR366313
33. [33] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966. Zbl0148.12601MR203473
34. [34] A. Klein, Quadratic Expressions in a Free Boson Field, Trans. Amer. Math. Soc., t. 181, 1973, p. 439-456. Zbl0266.47035MR406213
35. [35] J. Lebowitz, GHS and Other Inequalities, Commun. Math. Phys., t. 35, 1974, p. 87-92. MR339738
36. [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. MR312854
37. [37] J. Lebowitz and O. Penrose, Decay of Correlations, Phys. Rev. Lett., t. 31, 1973, p. 749-752. 
38. [38] A. Lenard and C. Newman, Infinite Volume Asymptotics in P(φ)2 Field Theory, Commun. Math. Phys., t. 39, 1974, p. 243-250. MR356776
39. [39] A.J. Lions, Lectures on Elliptic Partial Differential Equations, Tata Institute, 1967. Zbl0253.35001MR265732
40. [40] E. Nelson, Feynman Integrals and the Schrödinger Equation, J. Math. Phys., t. 5, 1964, p. 332-343. Zbl0133.22905MR161189
41. [41] E. Nelson, A Quartic Interaction in Two Dimensions, inMathematical Theory of Elementary Particles, ed. R. Goodman and I. Segal, M. I. T. Press, Cambridge, Mass.1966. MR210416
42. [42] E. Nelson, Quantum Fields and Markoff Fields, inPartial Differential Equations, Ed. D. Spencer, A. M. S., Providence, 1973. Zbl0279.60096MR337206
43. [43] E. Nelson, The Free Markoff Field, J. Func. Anal., t. 12, 1973, p. 211-227. Zbl0273.60079MR343816
44. [44] E. Nelson, Probability Theory and Euclidean Field Theory, in Constructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer-Verlag, 1973. Zbl0367.60108MR395513
45. [45] C. Newman, Gaussian Correlation Inequalities for FerromagnetsZ. Wahrscheinlichkeitstheorie verw. Gebiete , , t. 33, 1975, p. 75-93. Zbl0297.60053MR398401
46. [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). Zbl0181.56901MR241075
47. [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. MR403482
48. [48] J. Percus, Correlation Inequalities for Ising Spin Systems, Commun. Math. Phys., t. 40, 1975, p. 283-308. MR378683
49. [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. [50] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. I. Functional Analysis, Academic Press, New York, 1972. Zbl0242.46001
51. [51] D. Robinson, The Thermodynamic Pressure in Quantum Statistical Mechanics, Springer-Verlag, Berlin, 1971. MR432122
52. [52] L. Rosen, Renormalization of the Hilbert Space in the Mass Shift Model, J. Math. Phys., t. 13, 1972, p. 918-927. MR299127
53. [53] L. Rosen, Bose Field Theory as Classical Statistical Mechanics, II. The Lattice Approximation and Correlation Inequalities, inConstructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer-Verlag, 1973. 
54. [54] D. Ruelle, Statistical Mechanics, Benjamin, New York, 1969. Zbl0177.57301MR289084
55. [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. [56] I. Segal, Tensor Algebras over Hilbert Spaces, ITrans. Amer. Math. Soc., t. 81, 1956, p. 106-134. Zbl0070.34003MR76317
57. [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. Zbl0085.21806MR112626
58. [58] I. Segal, Non-linear Functions of Weak Processes, I. J. Func. Anal., t. 4, 1969, p. 404- 451. Zbl0187.39201
59. [59] I. Segal, Construction of Non-linear Local Quantum Processes, I. Ann. Math., t. 92, 1970, p. 462-481. Zbl0213.40904MR272306
60. [60] D. Shale, Linear Symmetries of the Free Boson Field, Trans. Amer. Math. Soc., t. 103, 1962, p. 149-167. Zbl0171.46901MR137504
61. [61] B. Simon, On the Glimm-Jaffe Linear Lower Bound in P(φ)2 Field TheoriesJ. Func. Anal., t. 10, 1972, p. 251-258. MR345563
62. [62] B. Simon, The P(φ)2 Euclidean (Quantum) Field Theory, Princeton Univ. Press, 1974. MR489552
63. [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. MR428998
64. [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. Zbl0241.47029MR293451
65. [65] P. Sodano, Thesis, University of Naples, 1974 (unpubl.). 
66. [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. MR363294
67. [67] G. Sylvester, Representations and Inequalities for Ising Model Ursell Functions, Commun. Math. Phys., t. 42, 1975, p. 209-220. MR406301

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