Spin and flavor projection operators in the SU (2Nf) spin-flavor group Article uri icon

abstract

  • The quadratic Casimir operator of the special unitary SU(N) group is used to construct projection operators, which can decompose any of its reducible finite-dimensional representation spaces contained in the tensor product of two and three adjoint spaces into irreducible components. Although the method is general enough, it is specialized to the SU(2Nf)→SU(2) - SU(Nf) spin-flavor symmetry group, which emerges in the baryon sector of QCD in the large-Nc limit, where Nf and Nc are the numbers of light quark flavors and color charges, respectively. The approach leads to the construction of spin and flavor projection operators that can be implemented in the analysis of the 1/Nc operator expansion. The use of projection operators allows one to successfully project out the desired components of a given operator and subtract off those that are not needed. Some explicit examples in SU(2) and SU(3) are detailed. © 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the https://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article%27s title, journal citation, and DOI. Funded by SCOAP3.
  • The quadratic Casimir operator of the special unitary SU(N) group is used to construct projection operators, which can decompose any of its reducible finite-dimensional representation spaces contained in the tensor product of two and three adjoint spaces into irreducible components. Although the method is general enough, it is specialized to the SU(2Nf)→SU(2) - SU(Nf) spin-flavor symmetry group, which emerges in the baryon sector of QCD in the large-Nc limit, where Nf and Nc are the numbers of light quark flavors and color charges, respectively. The approach leads to the construction of spin and flavor projection operators that can be implemented in the analysis of the 1/Nc operator expansion. The use of projection operators allows one to successfully project out the desired components of a given operator and subtract off those that are not needed. Some explicit examples in SU(2) and SU(3) are detailed. © 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the https://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.

publication date

  • 2020-01-01