Extension To Quantum Electrodynamics
Canonical quantization of the electromagnetic fields proceeds by elevating the scalar and vector potentials; φ(x), A(x), from fields to field operators. Substituting 1/c2 = ε0μ0 into the previous Lorenz gauge equations gives:
Here, J and ρ are the current and charge density of the matter field. If the matter field is taken so as to describe the interaction of electromagnetic fields with the Dirac electron given by the four-component Dirac spinor field ψ, the current and charge densities have form:
where α are the first three Dirac matrices. Using this, we can re-write Maxwell's equations as:
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Maxwell's equations (QED)
which is the form used in quantum electrodynamics.
Read more about this topic: Mathematical Descriptions Of The Electromagnetic Field, Potential Field Approach
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