Finite Dimensional Approximation and Pin(2)-equivariant Property for Rarita-Schwinger-Seiberg-Witten Equations

<p>The Rarita-Schwinger operator Q was initially proposed in the 1941 paper by Rarita and Schwinger to study wave functions of particles of spin 3/2, and there is a vast amount of physics literature on its properties. Roughly speaking, 3/2−spinors are spinor-valued 1-forms that also happen to be in the kernel of the Clifford multiplication. Let X be a simply connected Riemannian spin 4−manifold. Associated to a fixed spin structure on X, we define a Seiberg-Witten-like system of non-linear PDEs using Q and the Hodge-Dirac operator d∗ + d+ after suitable gauge-fixing. The moduli space of solutions M contains (3/2-spinors, purely imaginary 1-forms). Unlike in the case of Seiberg-Witten equations, solutions are hard to find or construct. However, by adapting the finite dimensional technique of Furuta, we provide a topological condition of X to ensure that M is non-compact; and thus, M contains infinitely many elements. </p>

Name thesis:degree_name

Doctor of Philosophy in Mathematics (PhD)

Level thesis:degree_level

Dissertation

Year dc:date.available

2022

Author dc:creator

• Nguyen, Minh Lam

Advisor dc:contributor.advisor

• Van Horn-Morris, Jeremy

Contributors dc:contributor

• Ryan, John
• Harrington, Phillip S.

• 11/8th conjecture
• Gauge theory
• geometric analysis
• low dimensional topology
• mathematical physics
• Rarita-Schwinger operator
• Seiberg-Witten theory
• Elementary Particles and Fields and String Theory
• Geometry and Topology
• Partial Differential Equations

Repository record dc:identifier

https://scholarworks.uark.edu/etd/4429

OAI identifier oai:identifier

oai:scholarworks.uark.edu:etd-5979