Generalized Lee-Wick Formulation from Higher Derivative Field Theories

Abstract

We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Till now, the AF Lagrangian has been studied only for N=2 and 3 cases, where $N$ is the number of poles of the two-point function of the HD scalar field. We construct the AF Lagrangian for arbitrary $N$. By the linear combinations of AF fields, we also obtain the corresponding LW form. We find the explicit mapping matrices among the HD fields, the AF fields, and the LW fields. As an exercise of our construction, we calculate the relations among parameters and mapping matrices for $N=2,3$, and 4 cases.

23 pages, version to appear in PRD, we improved the transformation from HD to LW in Subsection 3.1, added comments on gauge field related with AF Lagrangians in Conclusion, and added references

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• Generalized Uncertainty Principle as a Consequence of the Effective Field Theory
• External Sources in Lee-Wick Theories
• Higher Derivative Scalar Quantum Field Theory in Curved Spacetime
• Short distance modification of the quantum virial theorem
• LHC Constraints on the Lee-Wick Higgs Sector
• Interparticle potential energy for D-dimensional electromagnetic models from the corresponding scalar ones
• Acausality from a Dark Sector
• Scalar Perturbation in Symmetric Lee-Wick Bouncing Universe
• About the triviality of the higher derivative sector in the abelian Lee-Wick model
• Calculations in induced gravity from higher-derivative field theories