Renormalized Local Quantum Field Theory and Critical Behaviour
1. G. Mack, Kaiserslautern lectures 1972, Lecture Notes in Physics, Vol. 17, Springer Verlag
2. C. Di Castro, Lettere Nuovo Cim. 5, 69 (1972).
3. B. Schroer, “A Theory of Critical Phenomena based on the Normal Product Formalism”, FU Berlin preprint 1972.
4. E. Brezin, I. C. Guillou and J. Zinn-Justin, “Wilson Theory of Critical Phenomena and CallanSymanzik Equations in 4-ε Dimensions”. Saclay preprint.
5. P. K. Mitter, “Callan-Symanzik Equations and ε-Expansion”. University of Maryland Technical Report.
KeywordsAnomalous Dimension Critical Phenomenon Critical Theory Vertex Function Critical Index
Unable to display preview. Download preview PDF.
- 1.K.G. Wilson and J.Kogut, Institute for Advanced Study Lecture Notes C 0 0 2220–2 1972.Google Scholar
- 2.K. Osterwalder and R. Schrader, Havard University preprint 1972 and literature quoted therein.Google Scholar
- 4.For those of our mathematically minded collegues for which the word “identical” is too strong we refer to 2).Google Scholar
- 7.W. Zimmermann, Brandeis Lectures, Cambridge 1970.Google Scholar
- 8.J. H. Lowenstein and B. Schroer, NYU report 18172, to be published in the comment section of Phys. Rev.D.Google Scholar
- 9.M. Gomes and J. Lowenstein, Nucl. Phys. B, Sept. 1972.Google Scholar
- 10.See for example reference 7.Google Scholar
- 11.Y. M. Lam, University of Pittsburgh preprint, Sept.1972.Google Scholar
- 12.J. H. Lowenstein, University of Maryland Lecture Notes 1972. J. H. Lowenstein, Commun. Math. Phys. 24, (1971).Google Scholar
- 15.M. Gomes and J. H. Lowenstein, “Linear Relations among Normal Product Fields”, University of Pittsburgh preprint 1972.Google Scholar
- 18.J. T. Diatlov, V.V. Sudakov, K.A. Ter-Martirosian JETP 5, 631 (1957).Google Scholar
- 19.The following discussion is taken from Symanzik ref.17 with the slight, but for our purpose important modification, that our u normalization permits the direct identification with a u-normalized zero-mass theory.Google Scholar
- 20.B. Schroer, “A Theory of Critical Phenomena based on the Normal Product Formalism”, FU Berlin preprint 1972. See distinction between short-and long-distance scaling limits according to the slope of Q has been first discussed by G. Mack, Kaiserslautern Lectures, Lecture Notes in Physics Vol. 17, Springer Verlag.Google Scholar
- 21.E. Brezin, I.C. Guillon and J. Zinn-Justin, “Wilson Theory of Critical Phenomena and Callan-Symanzik Equations in 4-e Dimensions”, Saclay preprint. P.K. Mitter, “Callan-Symanzik Equations and a-Expansions”. University of Maryland Technical Report No. 73–020. The scale invariant correlation functions for statistical mechanics cannot be constructed by dilatation processes starting from the massive theory. The computational part of the determination of the critical indices is correct in these papers because the authors pick among the many scale invariant limits the one with anomalous dimension which moves continously into zero for ε → 0. The values of their critical coupling constant in 2nd order in a is different from our aλ0(ε) and cannot be used to construct the correlation function at the critical temperature.Google Scholar
- 22.A.I. Larkin and D.E. Khmel’nitzky, JETP 29, 1123 (1969). These authors obtain for logarithmic factors in the leading term. If perturbation theory is only done in the coefficients of the differential equations, one does not obtain a logarithm. Our statement is relevant for the critical correlation functions only if our idealized picture, which led to the elimination of the cut-off (lattice distance), is correct in 4 dimensions. Compare K. Symanzik, “On theories with Massless Particles” DESY preprint.Google Scholar
- 23.In the following we present the computation of critical indices directly for the m = 0 preasymptotic theory. This computation is simpler than the massive one in ref. 21.Google Scholar
- 24.K.G. Wilson, Phys. Rev. Letters 28, 548 (1972). E. Brezin, D.J. Wallace and K.G. Wilson, Phys. Rev. Letters 29, 591 (1972).Google Scholar
- 26.K. Symanzik, DESY preprint 1973.Google Scholar
- 27.G. Mack, Kaiserslautern lectures “Lecture Notes in Physics” Vol. 17, Springer Verlag, chapter 7, p. 314.Google Scholar
- 28.Private communication from J. Geicke, S. Meyer and R. Seiler.Google Scholar
- 29.J. Geicke and S. Meyer, FU Berlin preprint to be published in Phys. Letters.Google Scholar