Quantization of n coupled scalar field theory

Understand

We study a model of n coupled scalar fields in Minkowski spacetime where all masses degenerate, which is considered as a toy model of polycritical gravity on AdS spacetime.

• We quantize this model within the Becchi-Rouet-Stora-Tyutin (BRST) scheme by introducing n Faddeev-Popov (FP) ghost fields.
• Extending a BRST quartet generated by two scalars and two FP ghosts to n scalars and n FP ghosts, there remains a physical subspace with positive norm for odd n, but there exists only the vacuum for even n.
• This clearly shows a non-triviality of odd-higher order derivative scalar field theories.