Abstract
It is shown that relativistic many-body Hamiltonians and wave functions can be expressed systematically with Tracy-Singh products for partitioned matrices. The latter gives rise to the usual notion for a relativistic N-electron wave function: a column vector composed of 2N blocks, each of which consists of 2N components formed by the Kronecker products of N one-electron 2-spinors. Yet, the noncommutativity of the Tracy-Singh product dictates that the chosen serial ordering of electronic coordinates cannot be altered when antisymmetrizing a Tracy-Singh product of 4-spinors. It is further shown that such algebraic representation uncovers readily the internal symmetries of the relativistic Hamiltonians and wave functions, which are crucial for deriving the electron-electron coalescence conditions.
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Acknowledgements
The research of this work was supported by grants from the National Natural Science Foundation of China (Project Nos. 21033001, 21273011, 21290192, and 11471025).
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Shao, S., Li, Z., Liu, W. (2017). Basic Structures of RelativisticWave Functions. In: Liu, W. (eds) Handbook of Relativistic Quantum Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40766-6_7
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DOI: https://doi.org/10.1007/978-3-642-40766-6_7
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