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I'm familiar with the idea that coherent states of photons act like the classical electromagnetic field. I've ran across speculation about producing coherent states of other neutral bosonic particles like the $\pi^0$, and manipulating the field (see for instance this answer).

Apart from the practical feasibility of constructing the states I like that the coherent state representation emphasizes the field aspects of quantum fields rather than the particle aspects while still being quantum mechanical. So I am wondering if there is a sensible definition of coherent states for bosonic fields that are not their own antiparticle?

If you construct the coherent state of the particle without the corresponding antiparticle you run into problems with charge superselection because it is a superposition of different particle numbers. Also coherent states tend to be produced when neutral bosons interact with a classical source. Intuitively for charged bosons we would expect a classical source to kick up particle-antiparticle pairs. So I am wondering how this would be precisely defined and if we lose any of the nice properties of the coherent state for the neutral case.

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There is an extensive survey paper by Zhang, Feng, and Gilmore that discusses coherent states for many different systems, both from a theoretical and a practical point of view. In particular, their unitary coherent states can be used to model nonrelativistic $N$ electron systems in quantum chemistry.

It is less clear how to utilize coherent states in 4D relativistic quantum field theory, but they have been used in lower-dimensional relativistic toy QFTs.

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  • $\begingroup$ Thank you for the reference. I had meant to give you the best answer after I read it, but I had started thinking about other things by that point, and didn't come back to it until now. $\endgroup$ – octonion Apr 9 '16 at 21:19

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