Dissertation/Thesis Abstract

The lattice Faddeev Model
by Shmidheiser, Hans K., Ph.D., New York University, 2009, 98; 3380274
Abstract (Summary)

We describe a lattice version of the Faddeev Model for knotted solitons. We briefly mention the known results for the original Faddeev Model, including the 3/4-energy growth law and the existence results of Lin and Yang. Then we discuss numerical implementations of the model by Faddeev, Battye and Sutcliffe and Ward, motivating the theoretical study of the Lattice Faddeev Model. In particular, we will focus on how one computes a Hopf number for a nice map from R3 to S2 by sampling at integer lattice points Z3. Alternatively, we discuss how one can use this to assign Hopf numbers to a map from Z3 to S2. We then describe how this technique could be generalized to compute general topological invariants for maps between manifolds, given in terms of differential forms, by sampling at a discrete set of points. We characterize some of the function spaces involved in the Lattice Faddeev Model, and derive some energy estimates. Finally, we apply the techniques of Lin and Yang to the Lattice Faddeev Model, to obtain existence results.

Indexing (document details)
Advisor: Lin, Fanghua
Commitee: Hang, Fengbo, Kohn, Robert, Lin, Fanghua, Shatah, Jalal, Yang, Yisong
School: New York University
Department: Mathematics
School Location: United States -- New York
Source: DAI-B 70/12, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Faddeev model, Hopf number, Lattice field theory, Quantum field theory, Topology, Variational problem
Publication Number: 3380274
ISBN: 978-1-109-50687-7
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