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.
In @cite_21 @cite_30 Erdem, and in @cite_25 't Hooft and Nobbenhuis discuss a novel kind of symmetry transformation consisting of a rotation of real positional coordinates to the imaginary axis, with the aim of ruling out a cosmological constant. The rotated representation that these authors use for their non-relativistic particle toy modle is identical to the one we discuss in section for the indefinite inner product theory. These authors are particularly interested in the relationship between the real and imaginary coordinate representations. Since we study this relationship in detail in the present article, it is conceivable that our mathematical framework may have further applications in this direction.
@cite_30 @cite_21 @cite_25
2006504824 2008434812
We introduce a symmetry principle that forbids a bulk cosmological constant in six and ten dimensions. Then the symmetry is extended in six dimensions so that it insures absence of 4-dimensional cosmological constant induced by the six-dimensional curvature scalar, at least, for a class of metrics. A small cosmological constant may be induced in this scheme by breaking of the symmetry by a small amount. In this paper we study a new symmetry argument that results in a vacuum state with strictly vanishing vacuum energy. This argument exploits the well-known feature that de Sitter and Anti- de Sitter space are related by analytic continuation. When we drop boundary and hermiticity conditions on quantum fields, we get as many negative as positive energy states, which are related by transformations to complex space. The paper does not directly solve the cosmological constant problem, but explores a new direction that appears worthwhile.