  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
