The development of quantum electrodynamics (QED) as a theory involved building upon classical and quantum mechanics. The formulation of QED emerged as a result of combining quantum mechanics with special relativity and classical electromagnetism.
To derive QED, one typically starts with the principles of quantum mechanics and then incorporates the concepts and equations of classical electromagnetism. This approach allows for a consistent and comprehensive description of the behavior of electromagnetic fields and particles at the quantum level.
While it is conceivable that alternative approaches might exist, it is important to note that the current understanding of QED heavily relies on the mathematical framework and physical insights gained from classical and quantum mechanics. The historical development and success of QED are rooted in the progressive integration of these foundational theories.
Therefore, it is challenging to envision deriving QED directly without considering the significant contributions and insights provided by classical and quantum mechanics along the way.