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), 1205-1209

MSC (1970):
Primary 81A18, 60J25; Secondary 80A05, 46C10

DOI:
https://doi.org/10.1090/S0002-9904-1974-13680-3

MathSciNet review:
0356774

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References | Similar Articles | Additional Information

**1.**M. E. Fisher and J. L. Lebowitz,*Asymptotic free energy of a system with periodic boundary conditions*, Comm. Math. Phys. 19 (1970), 251-272. 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 self-coupled 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), 10-22. 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), 99-124. MR 39 #3781. MR**242450****10.**J. L. Lebowitz and O. Penrose,*Decay of correlations*, Phys. Rev. Lett. 31 (1973), 749-752.**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*, Springer-Verlag, Berlin, 1971. MR**432122****13.**I. Segal,*Nonlinear functions of weak processes*. I, II, J. Functional Analysis 4 (1969), 404-456; ibid. 6 (1970), 29-75. 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****16.**B. Simon and R. Griffiths,*The*(ø^{4})_{2}*field theory as a classical Ising model*, Comm. Math. Phys. 33 (1973), 145-164. 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, Springer-Verlag, Berlin, 1973. MR**395513**

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DOI:
https://doi.org/10.1090/S0002-9904-1974-13680-3