摘要:

It is shown that relativistic many-body Hamiltonians and wave functions can beexpressed 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 $2^N$ blocks, each of which consists of $2^N$ 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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