Continuum Modes of Nonlocal Field Theories

Abstract

A class of nonlocal Lorentzian quantum field theories is introduced in arXiv:1502.01655 and arXiv:1411.6513, where the d'Alembertian operator $\square$ is replaced by a non-analytic function of the d'Alembertian, $f(\square )$. This is inspired by the Causal Set program where such an evolution arises as the continuum limit of a wave equation on causal sets. The spectrum of these theories contains a continuum of massive excitations. This is perhaps the most important feature which leads to distinct/interesting phenomenology. In this paper, we study properties of the continuum massive modes in depth. We derive the path integral formulation of these theories. Meanwhile, this derivation introduces a dual picture in terms of local fields which clearly shows how continuum massive modes of the nonlocal field interact. The dual picture, in principle, provides a path to extension beyond scalar fields and addressing the issue of renormalization.

References in corpus (6)

• Generalized Causal Set d'Alembertians
• Nonlocal Scalar Quantum Field Theory from Causal Sets
• Quantum Gravity signatures in the Unruh effect
• Low energy signatures of nonlocal field theories
• Tests of Quantum Gravity-Induced Non-Locality via Opto-mechanical Experiments
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Cited by in corpus (7)

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• Probing string-inspired gravity with the inspiral-merger-ringdown consistency tests of gravitational waves
• Nonlocal field theory of quasiparticle scattering in dipolar Bose-Einstein condensates
• Casimir Effect for Nonlocal Field Theories with Continuum Massive Modes
• Lagrangian Formulation of an Infinite Derivative Real Scalar Field Theory in the Framework of the Covariant Kempf-Mangano Algebra in a $(D+1)$-dimensional Minkowski Space-time