Search

Under reasonable working assumptions including the polynomial boundedness, one proves the well-known Cerulus-Martin lower bound on how fast an elastic scattering amplitude can decrease in the hard-scattering regime. In this paper we consider two non-trivial extensions of the previous bound. (i) We generalize the assumption of polynomial boundedness by allowing amplitudes to exponentially grow for some complex momenta and prove a more general lower bound in the hard-scattering regime. (ii) We prove a new lower bound on elastic scattering amplitudes in the Regge regime, in both cases of polynomial and exponential boundedness. A bound on the Regge trajectory for negative momentum transfer squared is also derived. We discuss the relevance of our results for understanding gravitational scattering at the non-perturbative level and for constraining ultraviolet completions. In particular, we use the new bounds as probes of non-locality in black-hole formation, perturbative string theory, classicalization, Galileons, and infinite-derivative field theories, where both the polynomial boundedness and the Cerulus-Martin bound are violated.

We analyze the dynamics of neutrino Gaussian wave-packets, the damping of flavor oscillations and decoherence effects within the framework of extended theories of gravity. We show that, when the underlying description of the gravitational interaction admits a violation of the strong equivalence principle, the parameter quantifying such a violation modulates the wave-packet spreading, giving rise to potentially measurable effects in future neutrino experiments.

In this paper we study for the first time topological defects in the context of nonlocal field theories in which Lagrangians contain infinite-order differential operators. In particular, we analyze domain walls. Despite the complexity of non-linear infinite-order differential equations, we are able to find an approximate analytic solution. We first determine the asymptotic behavior of the nonlocal domain wall close to the vacua. Then, we find a linearized nonlocal solution by perturbing around the well-known local 'kink', and show that it is consistent with the asymptotic behavior. We develop a formalism to study the solution around the origin, and use it to verify the validity of the linearized solution. We find that nonlocality makes the width of the domain wall thinner, and the energy per unit area smaller as compared to the local case. For the specific domain wall solution under investigation we derive a theoretical constraint on the energy scale of nonlocality which must be larger than the corresponding symmetry-breaking scale. We also briefly comment on other topological defects like string and monopole.

The aim of the workshop Quantum Gravity, Higher Derivatives & Nonlocality (QGRAV-2021) was to assess our current understanding of the interplay between gravity and quantum mechanics, with particular attention to what is the main role of higher derivatives and nonlocality in the formulation of a consistent theory of quantum gravity, and whether they are really necessary to describe Nature at a fundamental level. The workshop had brought together various schools of thought, and besides talks numerous discussions were also held. In addition to focusing on formal aspects of several approaches, applications of higher derivatives arid non locality were also discussed in the context of cosmology and black-hole physics. In this preface article we present a concise explanation of the main problems underlying the quantization of gravity in the high-energy regime, briefly list several approaches that have been proposed so far, and also provide a gist of what was intensively discussed during the workshop.

In quantum field theory, a consistent prescription to define and deform integration contours in the complex energy plane is needed to evaluate loop integrals and compute scattering amplitudes. In some nonlocal field theories, including string field theory, interaction vertices contain transcendental functions of momenta that can diverge along certain complex directions, thus making it impossible to use standard techniques, such as Wick rotation, to perform loop integrals. The aim of this paper is to investigate the viability of several contour prescriptions in the presence of nonlocal vertices. We consider three “different” prescriptions and establish their (in)equivalence in local and nonlocal theories. In particular, we prove that all these prescriptions turn out to be equivalent in standard local theories, while this is not the case for nonlocal theories where amplitudes must be defined first in Euclidean space, and then analytically continued to Minkowski. We work at one-loop level and focus on the bubble diagram. In addition to proving general results for a large class of nonlocal theories, we show explicit calculations in a string-inspired nonlocal scalar model.