Non-perturbative Quantization of Phantom and Ghost Theories: Relating Definite and Indefinite Representations

Abstract

We investigate the non-perturbative quantization of phantom and ghost degrees of freedom by relating their representations in definite and indefinite inner product spaces. For a large class of potentials, we argue that the same physical information can be extracted from either representation. We provide a definition of the path integral for these theories, even in cases where the integrand may be exponentially unbounded, thereby removing some previous obstacles to their non-perturbative study. We apply our results to the study of ghost fields of Pauli-Villars and Lee-Wick type, and we show in the context of a toy model how to derive, from an exact non-perturbative path integral calculation, previously ad hoc prescriptions for Feynman diagram contour integrals in the presence of complex energies. We point out that the pole prescriptions obtained in ghost theories are opposite to what would have been expected if one had added conventional $i\epsilon$ convergence factors in the path integral.

56 pages, Latex2e, minor edits, to appear in IJMPA

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Cited by in corpus (15)

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• Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model
• A Higher-Derivative Lee-Wick Standard Model
• Free box^k Scalar Conformal Field Theory
• Minimal Lee-Wick Extension of the Standard Model
• Electroweak Precision Data and the Lee-Wick Standard Model
• One-Loop Renormalization of Lee-Wick Gauge Theory
• Higher-Derivative Lee-Wick Unification
• Constraints on the Lee-Wick Higgs Sector
• The process gg -> h_0 -> gamma gamma in the Lee-Wick Standard Model
• The rigged Hilbert space approach to the Gamow states
• The other Higgses, at resonance, in the Lee-Wick extension of the Standard Model
• Path Integrals for Potential Scattering
• Unitarity, Lorentz invariance and causality in Lee-Wick theories: An asymptotically safe completion of QED
• Path Integrals of the Vector Field --- Covariance of a Path Integral ---