Date

2021-9

Author

Özcan, Berk

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Our objective in this thesis is to compute the pair production rates for both bosons and fermions under the influence of non-abelian gauge fields on the manifolds $\mathbb{R}^{3,1} \equiv \mathbb{R}^2 \times \mathbb{R}^{1,1}$ and $S^2 \times \mathbb{R}^{1,1}$. We will compare the pair production rates of the spherical cases with the flat ones, and also compare the non-abelian cases with the abelian ones to see effects of both curvature and non-abelian field strength on the pair production. We first review the pair production process, i.e. the so-called Schwinger effect using the path integral formalism for bosonic spin-$0$ i.e. scalar fields and for fermions, spin-$1/2$ i.e. spinor fields, and also subsequently review the recent results obtained in the literature on $\mathbb{R}^{3,1}$ and $S^2 \times \mathbb{R}^{1,1}$ with abelian orthogonal uniform electric and magnetic fields. We then move on to generalize these results by the inclusion of a uniform non-abelian magnetic field due to an external $SU(2)$ gauge field. In doing so, we find the opportunity to compare the pair production rates on $\mathbb{R}^{3,1}$ and $S^2 \times \mathbb{R}^{1,1}$ with non-abelian field switched on, and also compare its influence to previously obtained results without the non-abelian field. Novel effects of the presence of the uniform non-abelian magnetic field together with the effects of constant positive curvature of the $S^2$-submanifold are emphasized.

Subject Keywords

Non-abelian Gauge Theory, Pair Production, Schwinger Effect, Landau Problem, Dirac Operator on Curved Spaces

URI

https://hdl.handle.net/11511/93040

Collections

Graduate School of Natural and Applied Sciences, Thesis