Exorcising ghosts in quantum gravity
- PDF / 340,947 Bytes
- 10 Pages / 439.37 x 666.142 pts Page_size
- 67 Downloads / 242 Views
Exorcising ghosts in quantum gravity Iberê Kuntz1,2,3,a 1 Center of Mathematics, Federal University of ABC, Santo André, Brazil 2 Dipartimento di Fisica e Astronomia, Università di Bologna, Via Irnerio 46, 40126 Bologna, Italy 3 I.N.F.N., Sezione di Bologna, IS - FLAG, Via B. Pichat 6/2, 40127 Bologna, Italy
Received: 20 August 2020 / Accepted: 20 October 2020 © The Author(s) 2020
Abstract We remark that Ostrogradsky ghosts in higher-derivative gravity, with a finite number of derivatives, are fictitious as they result from an unjustified truncation performed in a complete theory containing infinitely many curvature invariants. The apparent ghosts can then be projected out of the quadratic gravity spectrum by redefining the boundary conditions of the theory in terms of an integration contour that does not enclose the ghost poles. This procedure does not alter the renormalizability of the theory. One can thus use quadratic gravity as a quantum field theory of gravity that is both renormalizable and unitary. Despite the major advances in the quantization of gravity obtained in the past few decades, a deep understanding of quantum gravity in the UV remains a matter of debate. General relativity is known to be non-renormalizable, generating higher curvature invariants in the action, which are required for renormalization [1]. However, by introducing higher-derivative terms, ghosts inevitably appear in the spectrum unless the theory is treated under the effective field theory formalism where the higher derivatives are seen as perturbations [2,3]. The purpose of this paper is to remark that Ostrogradskian ghosts in higher-derivative gravity are only apparent when one truncates the infinite series of curvature invariants. We then show how these ghosts can be removed by means of a suitable boundary condition. The known issue with higher powers of the curvature invariants is due to Ostrogradsky theorem [4–6]. It states that any dynamical system described by differential equations containing time derivatives higher than second (but finite) order necessarily possesses unbounded energy solutions, dubbed ghosts. The existence of a ghost is not itself an issue, but it becomes a problem when the ghost field interacts with other sectors, which allows for the endless process of transmitting energy from healthy fields to the ghost. At the quantum level, negative energy states are sometimes traded by states with negative norm which is again problematic as it violates the optical theorem [7]. One simple way of evading Ostrogradsky theorem is with degenerate theories, such as f (R), but as we will see, functions of the Ricci scalar are not sufficient for renormalization [8]. We will show yet another way of evading Ostrogradsky theorem in quantum gravity. The idea of embedding higher-derivative gravity into a theory with infinite curvature invariants is not new. This idea has been in fact a steppingstone for the infinite derivative gravity, whose gravitational propagator is defined to be an entire function with a single pole at vanish
Data Loading...
