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Type of Document	Dissertation
Author	Caticha, Ariel
Author's Email Address	ariel AT albany.edu
URN	etd-09222005-135843
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-09222005-135843
Title	Changes of variables and the renormalization group
Degree	PhD
Option	Physics
Advisory Committee	Advisor Name Title Fredrik Zachariasen Committee Chair David Politzer Committee Member Michael C. Cross Committee Member Steven C. Frautschi Committee Member Thomas A. Tombrello Committee Member
Keywords	Renormalization Group Non-Abelian Gauge theories Changes of Variables in Path Integrals
Date of Defense	1985-05-21
Availability	unrestricted
Abstract NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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 Yang-Mills 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 one-loop 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 saddle-point approximation is exact. A lattice gauge theory is proposed for which the application of this RG formalism is straightforward.
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