Quantum Fields: Spin 0, 1/2, 1. Covariant Quantization of the Electromagnetic Field

Abstract

As we have stated several times, it is a fact that a theory based upon the wave function formalism, and with interactions given by potentials, does not provide a consistent description of physical reality. There are a number of reasons for this. Some are empirical: in any process at high energy, particles are created; therefore a wave function formalism, where the number of particles stays constant in time, will not be appropriate. Moreover, even if particles cannot be created because the energy is not sufficient, they may appear as quantum fluctuations provided the time they are present, Δt, and the energy fluctuation, ΔE, satisfy the Bohr-Heisenberg relation

$$\Delta t\,\Delta E \sim \hbar.$$