#### Title

Investigations in non-Abelian gauge theory

#### Date of Completion

January 1999

#### Keywords

Mathematics|Physics, Elementary Particles and High Energy

#### Degree

Ph.D.

#### Abstract

We consider two problems in this work. In the first problem, we show that in a non-Abelian *SU*(*N*) Yang-Mills Chern-Simons theory, broken from *SU*(3) to *SU*(2), the renormalized ratio of Chern-Simons coupling to the gauge coupling is 1/4π times an integer, appropriate for the unbroken *N* = 2 case. In the second problem, we construct states that implement Gauss's law, and construct gauge-invariant operator-valued gauge and spinor fields. We show that there is a unitary operator that transforms the Gauss's law operator (including quarks) for a non-Abelian gauge theory to the “pure glue” Gauss's law operator. We use the unitary operator that effects this transformation to also transform the Hamiltonian for QCD in the temporal (*A*_{ 0} = 0) gauge into a representation in which all fields (quark and gauge fields) are gauge-invariant. In this representation, the interaction between quarks and gluons is described completely by a nonlocal interaction involving quark color charge density that is the non-Abelian analog of the Coulomb interaction in QED, and another interaction between the transverse gauge-invariant gauge field and the transverse quark color-current density. ^

#### Recommended Citation

Chen, Lusheng, "Investigations in non-Abelian gauge theory" (1999). *Doctoral Dissertations*. AAI9949106.

https://digitalcommons.lib.uconn.edu/dissertations/AAI9949106