Given a higher derivative classical/quantum field theory with say one scalar field, particularly the Lee-Wick standard model. It has been shown that such a field theory encompasses two kinds of fields, one normal and other a ghost field, in a particular limit, generally the high mass limit of the ghost field. We started with a single field but in ended up with a two particle field theory.
This makes me ask:
Is there any general mathematical theorem by which we can show that a $n$th order derivative theory(scalar, spinor or vector) can be quantized into $n$ different kind of particles? Has it got to do something with the symmtries involved in the theory?
And what is the physical importance of the constraint? And how exactly is the system behaving when that constraint is not satisfied?(It seems to be in some sort of a enmeshed state of the two particles.)
My question mainly relies on the paper in the following link [The Lee-Wick standard model]: http://arxiv.org/abs/0704.1845 . In section 2 (A Toy Model) he considers a higher derivative Lagrangian eq.(1) for a scalar field $\phi$. And then introduces an auxiliary field $\tilde{\phi}$. And then it is shown that given the condition $M > 2m$, the Lagrangian sort of gets decoupled into two different fields. One normal field and other a ghost field, both interacting with each other.