Skip to main content

The Non-Perturbative Renormalization Of (λϕ4)3

  • Conference paper
Renormalization Theory

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 23))

  • 286 Accesses

Abstract

The λϕ4 model in three space-time dimensions provides us with one of the few examples of the success of renormalization theory that goes beyond perturbation theory. The counter-terms (over and above Wick ordering) required by the Euclidean Green’s functions are summarized in the table below.

Supported in part by the National Science Foundation under grant MPS 73-05037

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography for the lectures of J. Feldman, J. Fröhlich and E. Seiler

  1. S. Albeverio and R. Høegh-Krohn, Comm. Math. Phys. 30, 171, (1972).

    Article  ADS  Google Scholar 

  2. S. Albeverio, J. Funct. Anal. 16, 39, (1974)

    Article  MATH  Google Scholar 

  3. H. Borchers, contribution in the Proceedings of the International Colloquium on Mathematical Methods of Quantum Field Theory, Marseille (1975).

    Google Scholar 

  4. D. Brydges, J. Math. Phys., 16, 1649 (1975) and “Boundedness Below for Fermion Model Theories, part II” University of Michigan preprint (1974).

    Google Scholar 

  5. D. Brydges and P. Federbush, J. Math. Phys. 15 730 (1974).

    Article  MathSciNet  ADS  Google Scholar 

  6. JT. Cannon, Comm. Math. Phys. 35, 215 (1974)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Ch] N. H. Christ and T. D. Lee, “Quantum Expansion of Soliton Solutions”, Columbia University, Preprint CO-2271–55, (1975); see also refs. therein.

    Google Scholar 

  8. P. Colella O. Lanford, “Sample Field Behavior for the Free Markov Field”, in Constructive Quantum Field Theory, eds. G. Velo AS. Wightman, Springer-Verlag (1973)

    Google Scholar 

  9. S. Coleman, Phys. Rev. D11, 2088, (1975)

    ADS  Google Scholar 

  10. R. Jackiw and L. Susskind, “Charge Shielding and Quark Confinement in the Massive Schwinger Model”, Ann. Phys., to appear.

    Google Scholar 

  11. [Da] R. Dashen, B, Hasslacher and A. Neveu, “The Particle Spectrum in Model Field Theories from Semi- classical Functional Integral Techniques”, Phys. Rev,, to appear.

    Google Scholar 

  12. DL] C. Deutsch M. Lavaud, Phys. Rev. A9, 2598, (1974)

    Article  ADS  Google Scholar 

  13. S. Doplicher, R. Haag and J. E. Roberts, Comm. Math. Phys. 23, 199, (1971) and 35, 49, (1974).

    Article  MathSciNet  ADS  Google Scholar 

  14. J. Dimock, Ann. Phys. 72, 177 (1972).

    Article  ADS  Google Scholar 

  15. J. Dimock, Comm. Math. Phys. 35, 347, (1974).

    MathSciNet  Google Scholar 

  16. J.-P, Eckmann, H. Epstein and J. Fröhlich, “Asymptotic Perturbation Expansion for the S-Matrix and the Definition of Time-Ordered Functions in Relativistic Quantum Field Models”, University of Geneva, Preprint, (1975).

    Google Scholar 

  17. EMS] J.-P. Eckmann, J. Magnen R. Seneor, Comm. Math. Phys. 39, 251 (1975)

    Article  MathSciNet  ADS  Google Scholar 

  18. L, Faddeev LA. Takhtajan, Theor. Math. Phys. 21, 160, (1974) and refs. given there; see also: L, Faddeev, “Quantization of Solitons”, IAS, Preprint, (1975).

    Google Scholar 

  19. Fe] J. Feldman, Comm. Math. Phys. 37, 93 (1974) and “Thesis”, Harvard University (1974)

    Article  MathSciNet  ADS  Google Scholar 

  20. FeO 1] J. Feldman and K. Osterwalder, “The Wightman Axioms and the Mass Gap for Weakly Coupled (Φ4)3 Quantum Field Theories”, Annals of Physics, to appear.

    Google Scholar 

  21. FeO 2] J. Feldman “The Construction of λϕ43 Quantum Field Models”, Proceedings of the International Colloquium on Mathematical Methods of Quantum Field Theory, Marseille, (1975) and work in preparation.

    Google Scholar 

  22. R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).

    Article  MathSciNet  ADS  Google Scholar 

  23. J. Fröhlich, Ann. Inst. Henri Poincaré, A21, 271, (1974),and “Schwinger Functions and Their Generating Functionals, II,” to appear in Adv. Math., (1975)

    Google Scholar 

  24. J. Fröhlich, “The Pure Phases, the Irreducible Quantum Fields and Dynamical Symmetry Breaking in Symanzik-Nelson positive Quantum Field Theories”, Princeton University, Preprint, (1975).

    Google Scholar 

  25. Fr 3] J. Fröhlich, Phys. Rev. Letters 34, 833, (1975), and paper in preparation.

    Article  ADS  Google Scholar 

  26. Fr 4] J. Fröhlich, “Classical and Quantum Statistical Mechanics in One and Two Dimensions: Two-Component Yukawa- and Coulomb Systems”, to appear in Comm. Math. Phys.

    Google Scholar 

  27. in Two dimensional Bose Quantum Field Models”, Princeton University, Preprint, (1975).

    Google Scholar 

  28. Fr S] J. Fröhlich and E. Seiler, “The Massive Thirring Schwinger Model: Convergence of Perturbation Theory in the Mass”, Preprint to appear.

    Google Scholar 

  29. I. Gel’fand and N. Vilenkin, Generalized Functions,Vol. 4, Applications of Harmonic Analysis, Academic Press, New York, 1964.

    MATH  Google Scholar 

  30. J. Ginibre, “Some applications of Functional Integration in Statistical Mechanics ” in Statistical Mechanics and Quantum Field Theory, eds. C. DeWitt R, Stora, Gordon and Breach (1971).

    Google Scholar 

  31. V. Glaser, Comm. Math, Phys. 37, 257, (1974).

    MathSciNet  MATH  Google Scholar 

  32. J. Glimm, Comm. Math. Phys. 5, 343 (1967) and 6, 61 (1967).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. J. Glimm, Comm. Math. Phys. 10, 1 (1968).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. J. Glimm and A. Jaffe, Ann. Phys. 60, 321 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  35. GJ 2] J. Glimm, J. Funct. Anal. 7, 323 (1971)

    Article  MathSciNet  Google Scholar 

  36. J. Glimm, Fortsch Physik 21, 327 (1973).

    Article  MathSciNet  Google Scholar 

  37. GJ 4] J. Glimm, On the Approach to the Critical Point”, Harvard University, Preprint, (1974)

    Google Scholar 

  38. J. Glimm T. Spencer, “The Particle Structure of the Weakly Coupled P(φ)2 Model and Other Applications of High Temperature Expansions,” in: Constructive Quantum Field Theory, ed. G. Velo and A. Wightman, Springer Lecture Notes in Physics, 1973.

    Google Scholar 

  39. GJS 2] J. Glimm, “Existence of Phase Transitions for φ24 Quantum Fields”, Proceedings of the International Colloquium on Mathematical Methods of Quantum Field Theory, Marseille (1975) and “Phase Transitions for φ24 Quantum Fields” Comm. Math. Phys. to appear and “A Cluster Expansion in the Two Phase Region” in preparation.

    Google Scholar 

  40. F. Guerra, Phys. Rev. Lett. 28, 1213, (1975).

    Article  Google Scholar 

  41. F, Guerra, L. Rosen B. Simon, Comm. Math, Phys. 27, 10, (1972) and 29, 233, (1973)

    Article  MathSciNet  ADS  Google Scholar 

  42. F. Guerra, Ann. Math. 101, 111, (1975).

    Article  MathSciNet  Google Scholar 

  43. F. Guerra, “Boundary Conditions in the P(φ)2 Euclidean Quantum Field Theory”, Princeton University,

    Google Scholar 

  44. P. R. Haimos, Measure Theory, Van Nostrand, New York (1950).

    Google Scholar 

  45. I. Herbst, “Remarks on Canonical Quantum Field Theory”, paper in preparation.

    Google Scholar 

  46. R. Høegh-Krohn, Comm. Math. Phys. 38, 195, (1974).

    Google Scholar 

  47. R. Jost, “The General Theory of Quantized Fields”, American Math. Soc., Pubi. 1965, Providence, R.I.

    Google Scholar 

  48. J. Lowenstein and A. Swieca, Ann. Phys. (N. Y.) 68, 172, (1971).

    Article  MathSciNet  ADS  Google Scholar 

  49. A. Luther and V. J. Emery, Phys. Rev. Lett., 33, 589, (1974).

    Article  ADS  Google Scholar 

  50. MS] J. Magnen and R. Seneor, “The Infinite Volume Limit of the φ43Model”, to appear in Ann. Inst. Henri Poincaré.

    Google Scholar 

  51. P. T. Matthews and A. Salam, Nuovo Cim. 12., 563 (1954) and 2, 120 (1955).

    Article  MathSciNet  MATH  Google Scholar 

  52. R. May, Physics Letters 25A, 282, (1967).

    Article  Google Scholar 

  53. Mc 1] O. A. McBryan, “Finite Mass Renormalizations in the Euclidean Yukawa2 Field Theory”, Comm. Math. Phys., to appear.

    Google Scholar 

  54. Mc 2] O. A. McBryan, “Volume Dependence of Schwinger Functions in the Yukawa2 Quantum Field Theory”, Comm. Math. Phys., to appear.

    Google Scholar 

  55. O. A. McBryan, “Convergence of the Vacuum Energy Density, φ-bounds and Existence of Wightman Functions for the Yukawa Model”, Rockefeller University preprint (1975).

    Google Scholar 

  56. O. A. McBryan and Y. M. Park, J. Math. Phys. 16, 104 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  57. Mi] R, Minlos, Tr. MoskO Mat. Obs. 8, 471, (1959), see also [GV] vol. 4„

    Google Scholar 

  58. H. Mitter, Z. f. Naturforschung 20a, 1505 (1965).

    MathSciNet  ADS  Google Scholar 

  59. E. Nelson, “Quantum Fields and Markov Fields”, in Proceedings of the Summer Inst, on Part. Diff. Equ., Berkeley 1971, American Math. Soc., Publ. 1973, Providence, R. I.

    Google Scholar 

  60. E. Nelson, J. Funct. Anal. 12, 211, (1973).

    Article  MATH  Google Scholar 

  61. E. Nelson, “Probability Theory and Euclidean Field Theory”, in Constructive Quantum Field Theory, G. Velo and A. S, Wightman (eds.), Lecture Notes in Physics 25, Springer-Verlag, Berlin-Heidelberg-New York, (1973).

    Google Scholar 

  62. K. Osterwalder and R. Schrader, Comm. Math. Phys. 31, 83, (1973) and 42, 281, (1975).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  63. K. Osterwalder, Helv. Phys. Acta 46, 272, (1973).

    MathSciNet  Google Scholar 

  64. Pa] Y. Park, “Lattice Approximation of the (φ4-μφ)3 Field Theory” to appear in J9 Math. Phys., and “The Xcp3 Euclidean Quantum Field Theory in a Periodic Box”, Yonsei University preprint.

    Google Scholar 

  65. J. Preskill, Princeton University Senior Thesis (1975)

    Google Scholar 

  66. R. Schrader, Ann. Phys. 70, 412, (1972).

    Article  MathSciNet  ADS  Google Scholar 

  67. J. Schwinger, Phys. Rev. 93, 615 (1953) and 128, 2425, (1962).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  68. E. Seiler, Comm. Math. Phys. 42, 163 (1975).

    MathSciNet  Google Scholar 

  69. SeS 1] E. Seiler and B. Simon, “On Finite Mass Renormalizations in the Two-dimensional Yukawa Model”, J. Math. Phys., to appear.

    Google Scholar 

  70. Ses 2] E. Seiler, “Bounds in the Yukawa Quantum Field Theory: Upper Bound on the Pressure, Hamiltonian Bound and Linear Lower Bound”, Comm. Math. Phys., to appear.

    Google Scholar 

  71. SeS 3] E. Seiler, “Nelson’s Symmetry and All That in the Yukawa2 and (φ4)3 Field Theories”, Princeton University preprint (in preparation).

    Google Scholar 

  72. Field Theory”, Princeton Series in Physics, Princeton University Press, (1974).

    Google Scholar 

  73. B. Simon, “Notes on Infinite Determinants of Hilbert Space Operators”, Princeton University preprint (1975).

    Google Scholar 

  74. T. Spencer, Comm. Math. Phys. 39, 63 (1974).

    Google Scholar 

  75. R. Streater A. Wightman, PCT, Spin, Statistics and All That, Benjamin, New York, 1964.

    Google Scholar 

  76. K. Symanzik, J. Mathc Phys. 7, 510, (1966), and “Euclidean Quantum Field Theory”, in Local Quantum Theory, Int. School of Physics ‘Enrico Fermi’, Course 45, R. Jost (ed. ), Academic Press, New York- London (1969).

    Article  MathSciNet  ADS  Google Scholar 

  77. AS Wightman, in Cargèse Lectures in Theor. Physics, Gordon & Breach, New York-London-Paris, (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1976 D. Reidel Publishing Company, Dordrecht-Holland

About this paper

Cite this paper

Feldman, J.S. (1976). The Non-Perturbative Renormalization Of (λϕ4)3 . In: Velo, G., Wightman, A.S. (eds) Renormalization Theory. NATO Advanced Study Institutes Series, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1490-8_14

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-1490-8_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1492-2

  • Online ISBN: 978-94-010-1490-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics