What is a quantum field theory?
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- by David C. Brydges PDF
- Bull. Amer. Math. Soc. 8 (1983), 31-40
References
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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.
- 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
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- Edward Nelson, Construction of quantum fields from Markoff fields, J. Functional Analysis 12 (1973), 97–112. MR 0343815, DOI 10.1016/0022-1236(73)90091-8 5. J. Fröhlich, On the triviality of $łambda \varphi ^{4}\sbd$ theories and the approach to the critical point in $d{>atop (—)}4$ dimensions, Inst. Hautes Études Sci., preprint. See also [13].
- 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, DOI 10.1007/BF01947075
- 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 496278, DOI 10.1007/BF01940332
- James Glimm and Arthur Jaffe, Quantum physics, Springer-Verlag, New York-Berlin, 1981. A functional integral point of view. MR 628000, DOI 10.1007/978-1-4684-0121-9
- 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
- Barry Simon, The $P(\phi )_{2}$ Euclidean (quantum) field theory, Princeton Series in Physics, Princeton University Press, Princeton, N.J., 1974. MR 0489552
- 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, DOI 10.1007/BFb0018202 12. D. Brydges, J. Fröhlich and A. Sokal, A new construction of $\varphi _{3}^{4}$ (in preparation).
- Michael Aizenman, Proof of the triviality of $\varphi _{d}^{4}$ field theory and some mean-field features of Ising models for $d>4$, Phys. Rev. Lett. 47 (1981), no. 1, 1–4. MR 620135, DOI 10.1103/PhysRevLett.47.1
Additional Information
- Journal: Bull. Amer. Math. Soc. 8 (1983), 31-40
- MSC (1980): Primary 81E05, 81E10
- DOI: https://doi.org/10.1090/S0273-0979-1983-15076-0
- MathSciNet review: 682819