Symbolic-Numeric Algorithms for Computing Orthonormal Bases of SU(3) Group for Orbital Angular Momentum

We have developed symbolic-numeric algorithms implemented in the Wolfram Mathematica to compute the orthonormal canonical Gel’fand–Tseitlin (G-T), non-canonical Bargmann-Moshinsky (B-M) and Elliott (E) bases of irreducible representations SU(3) ⊃ SO(3) ⊃ SO(2) group for a given orbital of angular momentum. The algorithms resolve the missing label problem by solving eigenvalue problem for the “labeling” B-M operator X(3 ). The effective numeric algorithm for construction of the G-T basis provides a unique capability to perform large scale calculations even with 8 byte real numbers. The algorithms for the construction of B-M and E bases implemented very fast modified Gramm–Schmidt orthonormalization procedure. In B-M basis, a very effective formula for calculation of the matrix X(3 ) is derived by graphical method. The implemented algorithm for construction of the B-M basis makes it possible to perform large scale exact as well as arbitrary precision calculations. The algorithm for the construction of the E basis resolves the missing label problem by calculation of the matrix X(3 ) in an orthogonal basis from this matrix previously built in non-orthogonal basis. The implementation of this algorithm provides large scale calculations with arbitrary precision. © 2021, Springer Nature Switzerland AG.

Deveikis A.1 , Gusev A.2 , Vinitsky S. 2, 3 , Góźdź A. 4 , Pȩdrak A. 5 , Burdik Č.6 , Pogosyan G.7
Springer Science and Business Media Deutschland GmbH
12865 LNCS
  • 1 Vytautas Magnus University, Kaunas, Lithuania
  • 2 Joint Institute for Nuclear Research, Dubna, Russian Federation
  • 3 RUDN University, 6 Miklukho-Maklaya, Moscow, 117198, Russian Federation
  • 4 Institute of Physics, Maria Curie-Skłodowska University, Lublin, Poland
  • 5 National Centre for Nuclear Research, Warsaw, Poland
  • 6 Czech Technical University, Prague, Czech Republic
  • 7 Yerevan State University, Yerevan, Armenia
Bargmann–Moshinsky basis; Elliott basis; Gel’fand–Tseitlin basis; Gram–Schmidt orthonormalization; Irreducible representations; Missing label problem; Orthonormal non-canonical basis; SU(3) ⊃ SO(3) ⊃ SO(2)
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