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An algebraic projection procedure for construction of the basis vectors of irreducible representations of U(4) in the Su\(_{S}\)(2)\(\otimes \)su\(_{T}\)(2) basis

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Abstract

An effective algebraic spin–isospin projection procedure for constructing basis vectors of irreducible representations of U(4)\(\supset \)SU\(_{S}\)(2)\(\otimes \)SU\(_{T}\)(2) from those in the canonical U(4)\(\supset \)U(3)\(\supset \)U(2)\(\supset \)U(1) basis is proposed. It is shown that the expansion coefficients are components of null space vectors of the spin–isospin projection matrix. Explicit formulae for evaluating SU\(_{S}\)(2)\(\otimes \)SU\(_{T}\)(2) reduced matrix elements of U(4) generators are derived. Hence, matrix representations of U(4) in the noncanonical SU\(_{S}\)(2)\(\otimes \)SU\(_{T}\)(2) basis are determined completely.

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Data availability

Two Mathematica notebook files, P-Matrix-V1.1.nb for generating the projection matrix \(\textbf{P}\) with the corresponding expansion coefficients \(\textbf{c}^{(\zeta )}\) and U4-reduced-matrix\(-\)1.0.nb for calculating the reduced matrix elements of the U(4) generators, are provided as Supplementary Material to this paper.

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Acknowledgements

Support from the National Natural Science Foundation of China (12175097, 12175066) is acknowledged.

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Authors and Affiliations

  1. Department of Physics, Liaoning Normal University, Dalian, 116029, China

    Feng Pan, Yingxin Wu, Aoxue Li & Yuqing Zhang

  2. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, 70803-4001, USA

    Feng Pan & J. P. Draayer

  3. Department of Physics, School of Science, Huzhou University, Huzhou, Zhejiang, 313000, China

    Lianrong Dai

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  1. Feng Pan
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Correspondence to Feng Pan.

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Pan, F., Wu, Y., Li, A. et al. An algebraic projection procedure for construction of the basis vectors of irreducible representations of U(4) in the Su\(_{S}\)(2)\(\otimes \)su\(_{T}\)(2) basis. Eur. Phys. J. Plus 138, 662 (2023). https://doi.org/10.1140/epjp/s13360-023-04261-1

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