Nonperturbative methods in quantum field theory
Abstract
It is becoming increasingly important to develop methods to evaluate field theory outside the region of validity of perturbative expansions. For example, it is well known in the standard electroweak model that the magnitude of the scalar self coupling is set by the physical scalar Higgs mass. This mass is constrained by the triviality bound caused by the Gaussian trivial fixed point of the model which has been calculated in perturbation theory to be on the order of 1 TeV. However this limit occurs in the nonperturbative regime of the scalar self coupling and so requires treatment in a nonperturbative framework. Part One approaches this nonperturbative aspect of the standard electroweak model using Wilson renormalization group techniques. Restricting attention to the Higg's scalar and top quark degrees of freedom, nonperturbative triviality and vacuum stability mass bounds are calculated and compared to results obtained by lattice simulations and 1/N expansions. Part Two addresses the nonperturbative problem using effective Lagrangians. It is possible to represent the effects of a high energy, nonperturbative field theory in the low energy limit by an effective Lagrangian that is expanded in powers of momentum. From this, the coefficients of the leading and subleading operators that parameterize the nonperturbative effects of the high energy theory can be calculated. Such examinations have already been completed for the standard electroweak model and they are reviewed. An introduction to effective supersymmetric theories is given and an operator analysis is performed for a supersymmetric nonlinear sigma model from a geometrical viewpoint.
Degree
Ph.D.
Advisors
Clark, Purdue University.
Subject Area
Particle physics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.