- #1

hyperkahler

- 2

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I was thinking about how to implement a similar idea for nonlinear sigma models so that standard perturbation theory methods via Feynman diagrams are applicable. In particular consider the [itex]CP(N-1)[/itex] model:

[tex]

L= \frac{2}{g^2}[(\partial_\mu n^{\dagger})(\partial^\mu n)+(n^\dagger \partial_\mu n)^2]

[/tex]

where [itex] n [/itex] is a N-component vector of complex scalars with the constrained [itex] n^\dagger n=1 [/itex]. My problem is that this constraint leads to a new lagrangian term [itex] \lambda(n^\dagger n-1) [/itex] (introducing an auxiliary field [itex] \lambda [/itex] as lagrangian multiplier). The new field however is non propagating. Is there any way to correct this or do you know any other way how to quantize this type of system?