In Chaps. 3, 4, and 5, we saw that for each spin type, the Schrödinger picture wave equation for a state and the Heisenberg picture wave equation for the associated quantum field had the same form. In the former case, the wave equation solution was a state, i.e., a particle wave function. In the latter, the wave equation solution was a quantum field, i.e., an operator that created and destroyed states. For free scalars, this equation was the Klein-Gordon equation; for spinors, it was the (no interactions) Dirac equation; and for massless vectors (photons), it was Maxwell’s equation (sourceless, in terms of A^μ).

The result is zero expectation value for φ, and this would be true for whatever state, including the vacuum, that we choose. This effectively means that we would measure nothing if we tried to measure the quantum field φ. The field itself is unmeasurable.

Quantum field

Meaning

Noun