Basic structures of relativistic wave functions

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.