Group Theory & Strong Force Flashcards
What is the transformation and algebra of SO(3)?
What is the transformation, generators & algebra of SU(2)?
What are the generators & algebra of SU(3). What is the trace of two generators (over colour)?
What is the Casmir operator (in the fundamental & adjoint representation)?
It’s the sum of squares of generators. Proportional to the identity (Schur’s Lemma).
What are the Casmir operators (fundamental & adjoint) in SU(3)?
They relate to the strengths of quark/gluon and gluon/gluon couplings respectively.
What is the transformation operator for SU(3) rotations?
What new potentials & field tensors change under SU(3) rotations?
How does the covariant differential transform under SU(3) rotations?
What is the covariant differential for SU(3) symmetric fields?
What is the field strength tensor in QCD?
What is the full QCD Lagrangian?
What are the QCD Feynamn rule dependecies on g?
What is the Jacobi identity?
What is the Fierz identity (mathematically & pictorially)?
What is the QCD running coupling?
Explain how vacuum polarisations lead to the strong running coupling.
What is the general decomposition of a matrix, in terms of the indentity & generators?
What is the mapping of the fundamental generators to the adjoint space represented as?
What is the leading-order term for the strong beta-function?
Given the differential equation for running coupling, derive the equation that describes coupling strength down to a certain cut-off energy.
How do gluon potentials transform?
Given the transformation of the gluon potentials, show that gluons transform in the adjoint representation.
