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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

Information

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

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