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Estimates on Renormalization Group Transformations

Published online by Cambridge University Press:  20 November 2018

D. Brydges ,
J. Dimock  and
T. R. Hurd
D. Brydges
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA 22903 USA
J. Dimock
Affiliation:
Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1
T. R. Hurd
Affiliation:
Department of Mathematics SUNY at Buffalo, Buffalo, NY 14214, USA
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Abstract

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We consider a specific realization of the renormalization group $(\text{RG})$ transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultra-violet cutoff Gaussian measure. The new and improved definitions and estimates we present are sufficiently general and powerful to allow iteration of the transformation, hence the analysis of complete renormalization group flows, and hence the construction of a variety of scalar quantum field theories.

Keywords

81T0881T17
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 4 , 01 August 1998 , pp. 756 - 793
Copyright
Copyright © Canadian Mathematical Society 1998

References

[AR96] Abdessalam, M. and Rivasseau, V., An explicit large versus small field multiscale cluster expansion. Unpublished, 1996.Google Scholar
[BDH94a] Brydges, D., Dimock, J. and Hurd, T. R., Applications of the renormalization group. In:Mathematical Quantum Theory I: Field Theory and Many-body Theory (Eds. Feldman, J., Froese, R. and L. Rosen). AMS, Providence, RI, 1994.Google Scholar
[BDH94b] Brydges, D., Weak perturbations of Gaussian measures. In: Mathematical Quantum Theory I: Field Theory and Many-body Theory (Eds. Feldman, J., Froese, R. and L. Rosen). AMS, Providence, RI, 1994.Google Scholar
[BDH95] Brydges, D., The short distance behavior of ɸ43. Commun. Math. Phys. 172(1995), 143–186.Google Scholar
[BDH98] Brydges, D., A non-Gaussian fixed point for ɸ4 in 4 - ∈ dimensions. Commun. Math. Phys., 1998.(to appear).Google Scholar
[BK94] Brydges, D. C. and Keller, G., Correlation functions of general observables in dipole type systems I: Accurate upper bounds. Helv. Phys. Acta 67(1994), 43–116.Google Scholar
[BY90] Brydges, D. and Yau, H. T., Grad ß perturbations of massless Gaussian fields. Commun. Math. Phys. 129(1990), 351–392.Google Scholar
[DH91] Dimock, J. and Hurd, T.R., A renormalization group analysis of theKosterlitz-Thouless phase.Commun. Math. Phys. 137(1991), 263–287.Google Scholar
[DH92] Dimock, J., A renormalization group analysis of correlation functions for the dipole gas. J. Stat. Phys. 66(1992), 1277–1318.Google Scholar
[DH93] Dimock, J., Construction of the two-dimensional sine-Gordon model for β > 8π. Commun. Math. Phys. 156(1993), 547–580.+8π.+Commun.+Math.+Phys.+156(1993),+547–580.>Google Scholar
[GMLMS71] Gallavotti, G., Martin-Löf, A. and Miracle-Solé, S., Some problems connected with the description of the coexistence of phases at low temperature in the Ising model. In: Statistical Mechanics and Mathematical Problems (Ed. A. Lenard). Lecture Notes in Physics 20, Batelle Seattle Rencontres, Springer-Verlag, 1971.Google Scholar
[Rue69] Ruelle, D., Statistical Mechanics: Rigorous Results. Benjamin, New York, 1969.Google Scholar
[Sim79] Simon, B., Functional Integration and Quantum Physics. Academic Press, New York, 1979.Google Scholar
[SR72] Simon, B. and Reed, M., Methods of Modern Mathematical Physics I: Functional Analysis. Academic Press, San Diego, 1972.Google Scholar