This chapter applies the path integral formalism to quantum chromodynamics (QCD). It begins by discussing the need for color charge to resolve issues with the quark model and the spin-statistics theorem. The chapter reviews the core concepts of non-abelian gauge theory based on the SU(3) group, including its generators and structure. The necessity of gauge fixing for non-abelian fields is addressed, introducing the Faddeev-Popov procedure which involves the concept of ghost fields to cancel unphysical degrees of freedom. Finally, the full path integral for QCD is constructed, and the resulting Feynman rules are established, which are essential for calculating interactions between quarks and gluons.

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Path Integral Formulation of Quantum Chromodynamics

  • Michael Strickland

摘要

This chapter applies the path integral formalism to quantum chromodynamics (QCD). It begins by discussing the need for color charge to resolve issues with the quark model and the spin-statistics theorem. The chapter reviews the core concepts of non-abelian gauge theory based on the SU(3) group, including its generators and structure. The necessity of gauge fixing for non-abelian fields is addressed, introducing the Faddeev-Popov procedure which involves the concept of ghost fields to cancel unphysical degrees of freedom. Finally, the full path integral for QCD is constructed, and the resulting Feynman rules are established, which are essential for calculating interactions between quarks and gluons.