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.**Michael E. Fisher and J. L. Lebowitz,*Asymptotic free energy of a system with periodic boundary conditions.*, Comm. Math. Phys.**19**(1970), 251–272. MR**0278675****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(𝜙)₂*, Comm. Math. Phys.**27**(1972), 10–22. MR**0311242****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**(1968/1969), 99–124. MR**0242450****10.**J. L. Lebowitz and O. Penrose,*Decay of correlations*, Phys. Rev. Lett. 31 (1973), 749-752.**11.**Edward Nelson,*Quantum fields and Markoff fields*, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 413–420. MR**0337206****12.**Derek W. Robinson,*The thermodynamic pressure in quantum statistical mechanics*, Springer-Verlag, Berlin-New York, 1971. Lecture Notes in Physics, Vol. 9. MR**0432122****13.**Irving Segal,*Nonlinear functions of weak processes. I*, J. Functional Analysis**4**(1969), 404–456. MR**0249061****14.**Barry Simon,*Correlation inequalitites and the mass gap in 𝑃(𝜙)₂. II. Uniqueness of the vacuum for a class of strongly coupled theories*, Ann. of Math. (2)**101**(1975), 260–267. MR**0373511**, https://doi.org/10.2307/1970990**15.**Barry Simon,*The 𝑃(𝜙)₂ Euclidean (quantum) field theory*, Princeton University Press, Princeton, N.J., 1974. Princeton Series in Physics. MR**0489552****16.**Barry Simon and Robert B. Griffiths,*The (𝜙⁴)₂ field theory as a classical Ising model*, Comm. Math. Phys.**33**(1973), 145–164. MR**0428998****17.**Thomas Spencer,*The mass gap for the 𝑃(𝜙)₂ quantum field model with a strong external field*, Comm. Math. Phys.**39**(1974), 63–76. MR**0363294****18.**G. Velo and A. Wightman (eds.),*Constructive quantum field theory*, Springer-Verlag, Berlin-New York, 1973. The 1973 “Ettore Majorana” International School of Mathematical Physics, Erice (Sicily), 26 July–5 August 1973; Lecture Notes in Physics, Vol. 25. MR**0395513**

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