Squeezed states electrodynamics

This result is a curious and troubling one for the prospect that there can be a classical B held that has real dynamics. This would imply that non-Abelian symmetry is determined by a Lagrangian of the form ( 32 — /i, 2J, where this is automatically zero by duality. However, if this were the case, we would still have non-Abelian symmetry as a nonLagrangian symmetry. This strongly supports the possibility that the electrodynamic vacuum will continue to exhibit non-Abelian symmetries, such as squeezed states, even if we impose E3 = B3 = 0. 

This suggests that electromagnetism may in fact have a deeper non-Abelian structure. In what follows it is assumed that the B(3 field exists. It is likely that the B 3 field exists only as a manifestation of nonlinear optics. This is an aspect of non-Abelian electrodynamics that has been quite under studied. Later, a discussion of squeezed state operators in connection to non-Abelian electrodynamics is mentioned. However, its role in nonlinear optics is an open topic for work. 

Squeezed States of the Radiation Field, Khalid Zaheer and M. Suhail Zubairy Cavity Quantum, Electrodynamics, E. A. Hinds... 

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