There is nothing artificial about particles as quanta of a field. Each finite-energy configuration of a quantum field may be written as a complex linear superposition of $N$-particle states with various values of $N$. A general and generic state in the Hilbert space isn't an eigenstate of the "number of particles operator" but that's true for any other observable, too: most states in the Hilbert space aren't eigenstates of a predetermined operator.

This is not a "problem"; it just means that if the observable expressed by the operator is measured, one may get different values as the result of the measurement. The probabilities of individual results are calculated using the standard quantum formula – the Born rule – as the squared absolute values of the complex probability amplitudes (inner products of the state vector with an eigenstate etc.).

In nonlinear field theories, one may often write down classical solutions called "solitons" which are stationary yet localized; there also exist quantum states in the Hilbert space whose support is close to the classical solution. Magnetic monopoles are a good example. Strictly speaking, the quantum states corresponding to these solitons may still be formally written down as combinations of the usual $N$-particle states but this way of writing them becomes useless because the nonlinearities in the equations of motion for the fields totally change the expected behavior relatively to a free field theory for which the $N$-particle-state basis is most useful.

If the fields are only excited by field modes with a long (macroscopic) wavelength, the interpretation in terms of ordinary particles becomes – in contrast with your expectations – most appropriate. The long wavelength is interpreted as the particles' having a very low momentum.

There is no "active field of research" of the type you suggest. Instead, the field you are describing is "learning the first classes in a basic undergraduate course of quantum mechanics". For example, if the dark matter is composed of neutralinos, they're the excitations of an ordinary fermionic field $\chi(x,y,z,t)$ transforming as a spinor, and the basis with $N$-particle states of several neutralinos with different momenta is a perfectly valid basis of the whole Hilbert space and it is therefore enough to describe anything that may physically occur to this field.

I have mentioned solitons. Dark matter could perhaps be made of solitons except that I am not aware of any viable models of this kind.

This post imported from StackExchange Physics at 2014-03-17 04:25 (UCT), posted by SE-user Luboš Motl