A direct basis approach to nonorthogonality in second quantization. Theory and application

We present a direct basis formalism for using nonorthogonal basis sets in the second quantization framework. As an alternative to the dual basis formalism, a direct basis retains the Hermiticity relation between the creation and annihilation operators, with which the form of quantum operators -- e.g. the number operator and the Hamiltonian -- can be readily interpreted and manipulated. To tackle the difficulty of formulating quantum operators in the direct basis, we introduce the coefficient matrix and the generalized creation and annihilation operators, with which an arbitrary N-particle operator can be generated by simple matrix manipulations with the metric tensor of a general basis set. We illustrate the application of the direct basis formalism with the Hubbard Hamiltonian and a dynamical study with the Heisenberg equations of motion