The weakly coupled Yukawa$_{2}$ field theory: cluster expansion and Wightman axioms
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- by Alan Cooper and Lon Rosen PDF
- Trans. Amer. Math. Soc. 234 (1977), 1-88 Request permission
Abstract:
We prove convergence of the Glimm-Jaffe-Spencer cluster expansion for the weakly coupled Yukawa model in two dimensions, thereby verifying the Wightman axioms including a positive mass gap.References
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M. Abramowitz and I. A. Stegun (Editors), Handbook of mathematical fonctions, with formulas, graphs, and mathematical tables, Nat. Bur. Standards Appl. Math. Ser., 55, U.S. Govt. Printing Office, Washington, D.C., 1964. MR 29 #4914.
- David C. Brydges, Cluster expansions for fermion fields by the time dependent Hamiltonian approach, J. Mathematical Phys. 17 (1976), no. 7, 1118–1124. MR 413864, DOI 10.1063/1.523037
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Jonathan Dimock and James Glimm, Measures on Schwartz distribution space and applications to $P(\phi )_{2}$ field theories, Advances in Math. 12 (1974), 58–83. MR 349171, DOI 10.1016/S0001-8708(74)80018-6
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745
- Joel S. Feldman and Konrad Osterwalder, The Wightman axioms and the mass gap for weakly coupled $(\Phi ^{4})_{3}$ quantum field theories, Ann. Physics 97 (1976), no. 1, 80–135. MR 416337, DOI 10.1016/0003-4916(76)90223-2
- Jürg Fröhlich, Schwinger functions and their generating functionals. I, Helv. Phys. Acta 47 (1974), 265–306. MR 436830
- G. Velo and A. Wightman (eds.), Constructive quantum field theory, Lecture Notes in Physics, Vol. 25, Springer-Verlag, Berlin-New York, 1973. The 1973 “Ettore Majorana” International School of Mathematical Physics, Erice (Sicily), 26 July–5 August 1973. MR 0395513 —, The particle structure of the weakly coupled $P{(\phi )_2}$ model and other applications of high temperature expansions. Part II: The cluster expansion, Constructive Quantum Field Theory (G. Velo and A. Wightman, Editors), Springer-Verlag, Berlin and New York, 1973, pp. 199-242.
- James Glimm, Arthur Jaffe, and Thomas Spencer, The Wightman axioms and particle structure in the ${\scr P}(\phi )_{2}$ quantum field model, Ann. of Math. (2) 100 (1974), 585–632. MR 363256, DOI 10.2307/1970959
- F. Guerra, L. Rosen, and B. Simon, The $\textbf {P}(\phi )_{2}$ Euclidean quantum field theory as classical statistical mechanics. I, II, Ann. of Math. (2) 101 (1975), 111–189; ibid. (2) 101 (1975), 191–259. MR 378670, DOI 10.2307/1970988 —, Boundary conations for the $P{(\phi )_2}$ Euclidean field theory, Ann. Inst. H. Poincaré A 25 (1976), 231-334. J. Magnen and R. Sénéor, The infinite volume limit of the $\phi _3^4$ model, Ann. Inst. H. Poincaré (to appear). —, The Wightman axioms for the weakly coupled Yukawa model in two dimensions, École Polytechnique (preprint).
- Oliver A. McBryan, Finite mass renormalizations in the Euclidean $\textrm {Yukawa}_{2}$ field theory, Comm. Math. Phys. 44 (1975), no. 3, 237–243. MR 398351, DOI 10.1007/BF01609828
- Oliver A. McBryan, Volume dependence of Schwinger function in the Yukawa$_{2}$ quantum field theory, Comm. Math. Phys. 45 (1975), no. 3, 279–294. MR 389075, DOI 10.1007/BF01608332 —, Contribution to Internat. Colloq. on Math. Methods of Quantum Field Theory, Marseille, 1975.
- Konrad Osterwalder and Robert Schrader, Euclidean Fermi fields and a Feynman-Kac formula for boson-fermion models, Helv. Phys. Acta 46 (1973/74), 277–302. MR 366276 —, Axioms for Euclidean Green’s functions. I, II, Comm. Math. Phys. 31 (1973), 83-112; ibid. 42 (1975), 281-305. MR 48#7834; 51 # 12189.
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419
- Lon Rosen, Renormalization of the Hilbert space in the mass shift model, J. Mathematical Phys. 13 (1972), 918–927. MR 299127, DOI 10.1063/1.1666077
- Erhard Seiler, Schwinger functions for the Yukawa model in two dimensions with space-time cutoff, Comm. Math. Phys. 42 (1975), 163–182. MR 376022, DOI 10.1007/BF01614159
- Erhard Seiler and Barry Simon, On finite mass renormalizations in the two-dimensional Yukawa model, J. Mathematical Phys. 16 (1975), no. 11, 2289–2293. MR 403484, DOI 10.1063/1.522458
- Erhard Seiler and Barry Simon, Bounds in the Yukawa2 quantum field theory: upper bound on the pressure, Hamiltonian bound and linear lower bound, Comm. Math. Phys. 45 (1975), no. 2, 99–114. MR 413886, DOI 10.1007/BF01629241
- E. Seiler and B. Simon, Nelson’s symmetry and all that in the Yukawa2 and $(\phi ^{4})_{3}$ field theories, Ann. Physics 97 (1976), no. 2, 470–518. MR 438960, DOI 10.1016/0003-4916(76)90044-0
- Barry Simon, The $P(\phi )_{2}$ Euclidean (quantum) field theory, Princeton Series in Physics, Princeton University Press, Princeton, N.J., 1974. MR 0489552
- Barry Simon, Notes on infinite determinants of Hilbert space operators, Advances in Math. 24 (1977), no. 3, 244–273. MR 482328, DOI 10.1016/0001-8708(77)90057-3
- Thomas Spencer, The mass gap for the $P(\phi )_{2}$ quantum field model with a strong external field, Comm. Math. Phys. 39 (1974), 63–76. MR 363294, DOI 10.1007/BF01609171
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- R. F. Streater and A. S. Wightman, PCT, spin and statistics, and all that, W. A. Benjamin, Inc., New York-Amsterdam, 1964. MR 0161603
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 234 (1977), 1-88
- MSC: Primary 81.47
- DOI: https://doi.org/10.1090/S0002-9947-1977-0468872-4
- MathSciNet review: 0468872