Explicit representation of Gel'fand–Tsetlin states in clifford algebra unitary group approach

Abstract

AbstractA explicit expression for the unitary group Clebsch–Gordan coefficients, which couple two fully antisymmetric single‐column states into the two‐column Gel'fand–Tsetlin states, is given in terms of isoscalar factors for the canonical subgroup chain U(n) ⊃ U(n – 1) ⊃ …︁ ⊃ U(1). The isoscalar factors are expressed through the step numbers labeling canonical basis states and enable a straightforward construction of Gel'fand–Tsetlin states in the Clifford algebra unitary group approach, without the use of the tables for the symmetric group outer‐product reduction coefficients.