We investigate the nonperturbative 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 nonperturbative 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 nonperturbative 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∊ convergence factors in the path integral.
Also related to the cosmological constant problem is the paper @cite_11 , which introduces phantom fields to cancel the ordinary matter contribution to the vacuum energy. Again, our non-perturbative approach to phantom fields may be useful in the study of these models.
@cite_11
1983032885
We study a symmetry, schematically Energy → — Energy, which suppresses matter contributions to the cosmological constant. The requisite negative energy fluctuations are identified with a ghost'' copy of the Standard Model. Gravity explicitly, but weakly, violates the symmetry, and naturalness requires General Relativity to break down at short distances with testable consequences. If this breakdown is accompanied by gravitational Lorentz-violation, the decay of flat spacetime by ghost production is acceptably slow. We show that inflation works in our scenario and can lead to the initial conditions required for standard Big Bang cosmology.