5
Let matter be!
Matter has always been and will always be one of the main objects of physics.
—Wolfgang Pauli [479]
When there are source charges, the quantization of the radiation field is a bit more subtle than what we saw in Chapter 2. For the free field, the classical dynamics is described completely by the sourceless Maxwell equations in the vacuum
Then both B and E are transverse. We have seen in Chapter 2 that in reciprocal space (mode space) we can easily identify a pair of canonically conjugate variables1 and construct a Hamiltonian with them.
The situation becomes more complicated as soon as charges are introduced. To start with, as the fields are described by Maxwell equations in the vacuum with sources
the electric field is no longer transverse. But even more important, ...
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