This thesis is, broadly speaking, on the subject of the Renormalization Group (RG), that is, the systematic means by which we understand how the physics of different energy or length scales interact with one another, and the dependence of physical quantities on the scale of their description. RG is of fundamental importance in the physical sciences; applications of RG range from the problem of modeling turbulence all the way to particle physics and quantum theories of gravity. RG grew out of quantum field theory, where it provided the conceptual tools necessary for a deeper understanding of renormalization, the apparent sensitivity of low-energy processes to high-energy physics. In statistical physics, RG played a central role in explaining the nontrivial phenomena associated with systems living at their critical points. By introducing the notion of fixed points in phase diagrams, RG was able to describe the origin of critical behavior.
The thesis that follows is, in particular, about new methods of achieving RG transformations, in both a continuum spacetime background and on a lattice discretization thereof. The subject is explored from the point of view of euclidean quantum field theory, or perhaps more accurately, statistical field theory. As a thesis grounded on the computational method of lattice simulation, I emphasize the role of lattice formulations throughout the work, especially in the first two chapters. In the first, I describe the essential aspects of lattice theory and its symbiosis with RG. In the second, I present a new, continuous approach to RG on the lattice, based on a numerical tool called Gradient Flow (GF). Simulation results from quartic scalar field theory in 2 and 3 dimensions (ϕ4d) and 4-dimensional 12-flavor SU(3) gauge theory, will be presented. In the third and fourth chapters, the focus becomes more analytic. Chapter 3 is an introductory review of Functional Renormalization Group (FRG). In chapter 4, I introduce the concept of Stochastic RG (SRG) by working out the relationship between FRG and stochastic processes.
|Commitee:||Neil, Ethan, DeGrand, Thomas, DeWolfe, Oliver, Pflaum, Markus|
|School:||University of Colorado at Boulder|
|School Location:||United States -- Colorado|
|Source:||DAI-B 82/2(E), Dissertation Abstracts International|
|Subjects:||Physics, Quantum physics, High Temperature Physics|
|Keywords:||High energy physics, Quantum field theory, Renormalization group, Statistical physics|
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