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What is a quantum field theory?
Author(s):
David C.
Brydges
Journal:
Bull. Amer. Math. Soc.
8
(1983),
31-40.
MSC (1980):
Primary 81E05, 81E10
MathSciNet review:
682819
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Additional information
References:
- 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.
- M. Reed and B. Simon, Methods of modern mathematical physics, Volumes I, II, Academic Press, New York, 1972, 1975. MR 751959
- 3.
- R. F. Streater and A. S. Wightman, PCT spin & statistics and all that, Benjamin, New York, 1964. MR 161603
- 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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81E05, 81E10
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(1980):
81E05, 81E10
Additional Information:
DOI:
10.1090/S0273-0979-1983-15076-0
PII:
S 0273-0979(1983)15076-0
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