Unitary matrix expansions of creation and annihilation operators

1 UNITARY MATRIX EXPANSIONS OF CREATION AND ANNIHILATION OPERATORS 

Let us begin by considering the relationship between spin-orbital transformations in first quantization and the transformations of creation operators in second quantization. Assume that we have constructed two Fock spaces, one from the set of first-quantization spin orbitals f p and another from the transformed set in (3.2.1). What is the relationship between the second-quantization creation operators of the two Fock spaces In the original spin-orbital basis, an N-electron Slater determinant in first quantization 

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