A formulation of discrete differential geometry applied to fermionic lattice field theory and its implications for chiral symmetry
Citation:
Steven Watterson, 'A formulation of discrete differential geometry applied to fermionic lattice field theory and its implications for chiral symmetry', [thesis], Trinity College (Dublin, Ireland). School of Mathematics, 2008, pp 141Download Item:
Watterson TCD THESIS 8353 A formulation.pdf (PDF) 72.46Mb
Abstract:
In this thesis, we develop the Geometric Discretization formulation of Dirac-Kahler fermions. We note that the naive definition of chiral synnnetry is only approximately captured in the formulation. However, we show that we can use the two complexes associated with the definition of the Hodge star to construct chiral projection operators that exactly project a different chirality of held on to each complex. Similarly, we construct flavour projection operators that project a different flavour of field on to each complex. We also see that, in two space-time dimensions, we need four complexes to simultaneously separate the chiral and flavour components of the field.
Author: Watterson, Steven
Advisor:
Peardon, MikeQualification name:
Doctor of Philosophy (Ph.D.)Publisher:
Trinity College (Dublin, Ireland). School of MathematicsNote:
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Mathematics, Ph.D., Ph.D. Trinity College DublinLicences: