The pressure is independent of the boundary conditions for $P\left( \phi \right)_2$ field theories
Authors:
F. Guerra, L. Rosen and B. Simon
Journal:
Bull. Amer. Math. Soc. 80 (1974), 12051209
MSC (1970):
Primary 81A18, 60J25; Secondary 80A05, 46C10
MathSciNet review:
0356774
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References 
Similar Articles 
Additional Information
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F. Guerra, L. Rosen and B. Simon, Correlation inequalities and the mass gap in P(ø)_{2}. III. Mass gap for a class of strongly coupled theories (in preparation).
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 1.
 M. E. Fisher and J. L. Lebowitz, Asymptotic free energy of a system with periodic boundary conditions, Comm. Math. Phys. 19 (1970), 251272. MR 43 #4405. MR 278675
 2.
 J. Ginibre, Some applications of functional integration in statistical mechanics, Statistical Mechanics and Quantum Field Theory, Les Houches 1970 (C. DeWitt and R. Stora, editors), Gordon and Breach, New York, 1971.
 3.
 J. Glimm and A. Jaffe, Quantum field models Statistical Mechanics and Quantum Field Theory, Les Houches, 1970 (C. DeWitt and R. Stora, editors), Gordon and Breach, New York, 1971.
 4.
 F. Guerra, Uniqueness of the vacuum energy density and Van Hove phenomenon in the infinite volume limit for two dimensional selfcoupled Bose fields, Phys. Rev. Lett. 28 (1972), 1213.
 5.
 F. Guerra, L. Rosen and B. Simon, Nelson's symmetry and the infinite volume behavior of the vacuum in P(ø)_{2}, Comm. Math. Phys. 27 (1972), 1022. MR 46 #10334. MR 311242
 6.
 F. Guerra, L. Rosen and B. Simon, The P(ø)_{2} Euclidean quantum field theory as classical statistical mechanics, Ann. of Math. (to appear).
 7.
 F. Guerra, L. Rosen and B. Simon, Boundary conditions in the P(ø)_{2} Euclidean quantum field theory (in preparation).
 8.
 F. Guerra, L. Rosen and B. Simon, Correlation inequalities and the mass gap in P(ø)_{2}. III. Mass gap for a class of strongly coupled theories (in preparation).
 9.
 J. L. Lebowitz and O. Penrose, Analytic and clustering properties of thermodynamic functions and distribution functions for classical lattice and continuum systems, Comm. Math. Phys. 11 (1968/69), 99124. MR 39 #3781. MR 242450
 10.
 J. L. Lebowitz and O. Penrose, Decay of correlations, Phys. Rev. Lett. 31 (1973), 749752.
 11.
 E. Nelson, Quantum fields and Markoff fields, Proc. Sympos. Pure Math., vol. 23, Amer. Math. Soc. Providence, R. I., 1973. MR 337206
 12.
 D. Robinson, The thermodynamic pressure in quantum statistical mechanics, SpringerVerlag, Berlin, 1971. MR 432122
 13.
 I. Segal, Nonlinear functions of weak processes. I, II, J. Functional Analysis 4 (1969), 404456; ibid. 6 (1970), 2975. MR 40 #2309; 41 #7974. MR 249061
 14.
 B. Simon, Correlation inequalities and the mass gap in P(ø)_{2}. II. Uniqueness of the vacuum for a class of strongly coupled theories, Ann. of Math. (to appear). MR 373511
 15.
 B. Simon, The P(ø^{4})_{2} Euclidean (quantum) field theory, Princeton Univ. Press, Princeton, N. J., 1974. MR 489552
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 B. Simon and R. Griffiths, The (ø^{4})_{2} field theory as a classical Ising model, Comm. Math. Phys. 33 (1973), 145164. MR 428998
 17.
 T. Spencer, The mass gap for the P(ø)_{2} quantum field model with a strong external field, Comm. Math. Phys. (to appear). MR 363294
 18.
 G. Velo and A. S. Wightman (editors), Constructive quantum field theory, Lectures Notes in Physics, vol. 25, SpringerVerlag, Berlin, 1973. MR 395513
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Additional Information
DOI:
http://dx.doi.org/10.1090/S000299041974136803
PII:
S 00029904(1974)136803
