Trace Operators for the State Labelling Problem in the Exceptional Lie Algebra F4

Abstract

The Casimir operators of the exceptional Lie algebra F4 are constructed using the method of trace operators. Taking into account a decomposition of matrices related to the embedding F4 _ so(9), subgroup scalars for the corresponding state labelling problem are determined as traces of powers of the components, enabling us to propose an orthonormal basis of states for each generic irreducible representation (IRREP) of F4. The basis of eigenstates for the IRREP [1000] of F4 is explicitly given.