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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)


What is a quantum field theory?

Author: David C. Brydges
Journal: Bull. Amer. Math. Soc. 8 (1983), 31-40
MSC (1980): Primary 81E05, 81E10
MathSciNet review: 682819
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References [Enhancements On Off] (What's this?)

  • 1. P. A. M. Dirac, Proc. Roy. Soc. 114 (1927). See also J. von Neumann, Mathematical foundations of quantum mechanics, Princeton Univ. Press, Princeton, N. J., 1955.
  • 2. Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959 (85e:46002)
  • 3. R. F. Streater and A. S. Wightman, PCT, spin and statistics, and all that, W. A. Benjamin, Inc., New York-Amsterdam, 1964. MR 0161603 (28 #4807)
  • 4. Edward Nelson, Construction of quantum fields from Markoff fields, J. Functional Analysis 12 (1973), 97–112. MR 0343815 (49 #8555)
  • 5. J. Fröhlich, On the triviality of $łambda \varphi \sp{4}\sbd$ theories and the approach to the critical point in $d{>atop (---)}4$ dimensions, Inst. Hautes Études Sci., preprint. See also [13].
  • 6. David Brydges, Jürg Fröhlich, and Thomas Spencer, The random walk representation of classical spin systems and correlation inequalities, Comm. Math. Phys. 83 (1982), no. 1, 123–150. MR 648362 (83i:82032)
  • 7. David Brydges and Paul Federbush, A lower bound for the mass of a random Gaussian lattice, Comm. Math. Phys. 62 (1978), no. 1, 79–82. MR 0496278 (58 #14843)
  • 8. James Glimm and Arthur Jaffe, Quantum physics, Springer-Verlag, New York-Berlin, 1981. A functional integral point of view. MR 628000 (83c:81001)
  • 9. Barry Simon, Functional integration and quantum physics, Pure and Applied Mathematics, vol. 86, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 544188 (84m:81066)
  • 10. Barry Simon, The 𝑃(𝜑)₂ Euclidean (quantum) field theory, Princeton University Press, Princeton, N.J., 1974. Princeton Series in Physics. MR 0489552 (58 #8968)
  • 11. Erhard Seiler, Gauge theories as a problem of constructive quantum field theory and statistical mechanics, Lecture Notes in Physics, vol. 159, Springer-Verlag, Berlin, 1982. MR 785937 (86g:81084)
  • 12. D. Brydges, J. Fröhlich and A. Sokal, A new construction of $\varphi \sb{3}\sp{4}$ (in preparation).
  • 13. Michael Aizenman, Proof of the triviality of 𝜙_{𝑑}⁴ field theory and some mean-field features of Ising models for 𝑑>4, Phys. Rev. Lett. 47 (1981), no. 1, 1–4. MR 620135 (82g:81048),

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PII: S 0273-0979(1983)15076-0

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