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Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box by Sergio M. Dutra

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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

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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

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the electric field is no longer transverse. But even more important, ...

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