Quantum Electrodynamics of Spin One‐Half and Spin Zero Particles in External Electrostatic Fields of Arbitrary Strength

We study in turn the quantum theories of an otherwise free electron‐positron field and of a charged pion field in the presence of the electrostatic field of an extended charge distribution of arbitrary strength. In both instances, the standard quantization fails because of an instability of the vacuum as it is usually defined. The character of the instability, different in each case, is analyzed, and it is shown how a consistent quantization can be carried out. The possible observation of the instabilities, which appears feasible for the electron‐positron field, is discussed.