TL;DR
This paper investigates a gauge-field-free Hamiltonian for Maxwell's equations, demonstrating its non-quantizability and emphasizing the essential role of gauge fields in quantum electrodynamics.
Contribution
It proves that simple electromagnetic field-only theories cannot be quantized, highlighting the necessity of gauge fields in QED.
Findings
The gauge-field-free Hamiltonian cannot be quantized.
No similar simple electromagnetic-only theories are quantizable.
Reinforces the importance of gauge fields in QED.
Abstract
We begin by studying a very simple Hamiltonian for Maxwell's equations that has no gauge fields and is made entirely of the electromagnetic fields. We then show that this theory cannot be quantized. We also show that no other such simple theory that only involves the electromagnetic fields can be quantized. This gives further evidence for the important role of gauge fields in QED.
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Taxonomy
TopicsPhotonic and Optical Devices