What is a quantum field theory?
David C. Brydges
Source: Bull. Amer. Math. Soc. (N.S.) Volume 8, Number 1 (1983), 31-40.
Primary Subjects: 81E05, 81E10
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bams/1183550013
Mathematical Reviews number (MathSciNet):
MR682819
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.
Zentralblatt MATH:
0242.46001
Mathematical Reviews (MathSciNet):
MR751959
3. R. F. Streater and A. S. Wightman, PCT spin & statistics and all that, Benjamin, New York, 1964.
Zentralblatt MATH:
0135.44305
Mathematical Reviews (MathSciNet):
MR161603
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.
Zentralblatt MATH:
0252.60053
Mathematical Reviews (MathSciNet):
MR343815
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.
Mathematical Reviews (MathSciNet):
MR648362
7. D. Brydges and P. Federbush, A lower bound for the mass of a random Gaussian lattice, Comm. Math. Phys. 62, 79 (1978).
Zentralblatt MATH:
0381.60059
Mathematical Reviews (MathSciNet):
MR496278
8. J. Glimm and A. Jaffe, Quantum physics, a functional integral point of view, Springer-Verlag, Berlin and New York, 1981. See also [10].
Zentralblatt MATH:
0461.46051
Mathematical Reviews (MathSciNet):
MR628000
9. G. Simon, Functional integration and quantum physics, Academic Press, New York, 1979.
Zentralblatt MATH:
0434.28013
Mathematical Reviews (MathSciNet):
MR544188
10. G. Simon, The P (ø)2 Euclidean quantum field theory, Princeton Univ. Press, Princeton, N. J., 1974.
Mathematical Reviews (MathSciNet):
MR489552
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).
Mathematical Reviews (MathSciNet):
MR785937
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).
Mathematical Reviews (MathSciNet):
MR620135
Bulletin (New Series) of the American Mathematical Society
