Citation
Caticha, Ariel (1985) Changes of variables and the renormalization group. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd09222005135843
Abstract
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A class of exact infinitesimal renormalization group (RG) transformations is studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a saddle point approximation is more accurate, becoming, in some cases, asymptotically exact as the transformations are iterated. The formalism provides a simplified and unified approach to several known renormalization groups. The RG equations for a scalar field theory are obtained and solved both by expanding in [...] and also by expanding in a single coupling constant. This calculation yields results in agreement with conventional methods.
Next we study the application of this kind of RG to YangMills theories. A simple exact gauge covariant RG transformation is constructed; the corresponding RG equations are obtained and solved in the weak coupling regime. This calculation shows that only certain initial conditions (i.e., bare actions) are compatible with the constraint that all the RG evolution be described by a single coupling constant. It also shows that at the tree level the [...] function for the SU(N) gauge theory is [...]. A oneloop calculation yields the usual result [...]. Unlike the scalar theory case the iteration of the RG transformation does not lead to an asymptotic situation in which the saddlepoint approximation is exact. A lattice gauge theory is proposed for which the application of this RG formalism is straightforward.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Changes of Variables in Path Integrals; NonAbelian Gauge theories; Renormalization Group 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  21 May 1985 
NonCaltech Author Email:  ariel (AT) albany.edu 
Record Number:  CaltechETD:etd09222005135843 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd09222005135843 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3694 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  23 Sep 2005 
Last Modified:  26 Dec 2012 03:02 
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