On the Topology of Nonlocal Field Theories of Material Continua

A fairly general and unified approach to nonlocality in material continua is introduced here. This work aims at proposing new mathematical and conceptual foundations for the emerging topic of nonlocal metamaterials suitable for physicists, engineers, mathematicians, and materials scientists. The text develops an original rigorous theory, a detailed example involving nonlocal semiconductor metamaterials, and extensive literature review and discussion of possible applications of nonlocal metamaterials.

On the Topology of Nonlocal Field Theories of Material Continua

A fairly general and unified approach to nonlocality in material continua is introduced here. This work aims at proposing new mathematical and conceptual foundations for the emerging topic of nonlocal metamaterials suitable for physicists, engineers, mathematicians, and materials scientists. The text develops an original rigorous theory, a detailed example involving nonlocal semiconductor metamaterials, and extensive literature review and discussion of possible applications of nonlocal metamaterials.

The Higgs mechanism in nonlocal field theory

We provide an example of nonlocal scalar electrodynamics that allows the same Higgs mechanism so successful in local field theory. The nonlocal action is structured in order to have the same exact solutions and the same equations of motion for perturbations of the local theory, at any perturbative order. Therefore, the perturbative degrees of freedom that propagate in the unstable vacuum are reshuffled when the stable vacuum is replaced in the EoM, but their number does not change at any perturbative order, and their properties are the same like in the usual local theory. Finally, the theory is superrenormalizable or finite at quantum level.

Nonlocal elastodynamics and fracture

A nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane elastodynamics associated with a running crack. We carry out our analysis for a plate subject to mode one loading. The length of the crack is prescribed a priori and is an increasing function of time.

Unattainability of the trans-Planckian regime in nonlocal quantum gravity

Based on the ultraviolet asymptotic freedom of nonlocal quantum gravity, we show that the trans-Planckian energy regime is unattainable in laboratory experiments. As physical implications, it turns out that the violation of causality, typical of nonlocal field theories, can never be detected in particle accelerators, while the asymptotic freedom of the theory provides an elegant solution to the so called trans-Planckian cosmological problem.