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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.
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  • 4. E. Nelson, Construction of quantum fields from Markov fields, J. Funct. Anal. 12 (1973), 97-112 and A quartic interaction in two dimensions, Mathematical Theory of Elementary Particles (R. Goodman and I. Segal (eds.)), MIT Press, Cambridge, Mass., 1966. MR 343815
  • 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. D. Brydges, J. Fröhlich and T. Spencer, The random walk representation of classical spin systems and correlation inequalities, Comm. Math. Phys. 83 (1982), 123. MR 648362
  • 7. D. Brydges and P. Federbush, A lower bound for the mass of a random Gaussian lattice, Comm. Math. Phys. 62, 79 (1978). MR 496278
  • 8. J. Glimm and A. Jaffe, Quantum physics, a functional integral point of view, Springer-Verlag, Berlin and New York, 1981. See also [10]. MR 628000
  • 9. G. Simon, Functional integration and quantum physics, Academic Press, New York, 1979. MR 544188
  • 10. G. Simon, The P (ø), Princeton Univ. Press, Princeton, N. J., 1974. MR 489552
  • 11. E. Seiler, Gauge theories as a problem of constructive quantum field theory and statistical mechanics, Troisième Cycle de la Physique Lecture Notes, 1981; Springer-Verlag, Berlin and New York (to appear). MR 785937
  • 12. D. Brydges, J. Fröhlich and A. Sokal, A new construction of $\varphi \sb{3}\sp{4}$ (in preparation).
  • 13. M. Aizenman, Proof of the triviality of $\varphi \sbd\sp{4}$ field theory and some mean field features of Ising models for d> 4, Phys. Rev. Lett, 47, 1 (1981). MR 620135

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