Self-consistent field method quantization

D. L. Yeager and M. K. Mishra, Int. J. Quantum Chem., 104, 871—879 (2005). Algebraic Modifications to Second Quantization for Non-Hermitian Complex Scaled Hamiltonians with Applications to a Quadratically Convergent Multiconfigurational Self-Consistent Field Method. 

Quantum electrodynamics requires the solution of the system (51) when a x), y/(x) and its adjoint (jc) are quantized fields. As a glance at any of the standard texts reveals, this involves many technical difficulties. Fortunately most of them do not affect the derivation of the DHFB method although they are unavoidable if we wish to go beyond self-consistent field approximations. 

The MFT equation of motion (25) can be derived in many ways, including the WKB approximation, the eikonal method, a (semi)classical time-dependent self-consistent field ansatz, density-matrix approaches, and the classical limit of algebraic quantization. Depending on the specific approach used, slightly different MFT schemes may result. For example, the classical force can be described either by the average of the quantum force as in Eq. (25) or by the derivative of the average quantum potential. 

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