Nonlocal and quasi-local field theories

Abstract

We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasi-local (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasi-local kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.

28 pages, 6 figures, LaTeX

References in corpus (8)

• Mass-gap for black hole formation in higher derivative and ghost free gravity
• Dynamics with Infinitely Many Derivatives: The Initial Value Problem
• Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model
• Universally Finite Gravitational & Gauge Theories
• Nonlocal quantum gravity and M-theory
• Nonlinear equations for p-adic open, closed, and open-closed strings
• On Some Nonlinear Integral Equation in the (Super)String Theory
• Spherical collapse of small masses in the ghost-free gravity

Cited by in corpus (102)

• Notes on non-singular models of black holes
• Locality & Entanglement in Table-Top Testing of the Quantum Nature of Linearized Gravity
• Occurrence of exact $R^2$ inflation in non-local UV-complete gravity
• Classical properties of non-local, ghost- and singularity-free gravity
• Super-renormalizable or Finite Lee-Wick Quantum Gravity
• Ghost-free infinite derivative quantum field theory
• Head-on collision of ultrarelativistic particles in ghost-free theories of gravity
• Consistent Higher Derivative Gravitational theories with stable de Sitter and Anti-de Sitter Backgrounds
• Quantum radiation from an evaporating non-singular black hole
• Spacetime completeness of non-singular black holes in conformal gravity
• Low-energy effects in a higher-derivative gravity model with real and complex massive poles
• A QCD analogy for quantum gravity
• The gravitational field of static p-branes in linearized ghost-free gravity
• Conformally-flat, non-singular static metric in infinite derivative gravity
• Towards nonsingular rotating compact object in ghost-free infinite derivative gravity
• Non-singular metric for an electrically charged point-source in ghost-free infinite derivative gravity
• Schwarzschild $1/r$-singularity is not permissible in ghost free quadratic curvature infinite derivative gravity
• Nonlocal star as a blackhole mimicker
• Gauge invariant renormalizability of quantum gravity
• Transmutation of nonlocal scale in infinite derivative field theories
• Black hole evaporation in conformal gravity
• Generalized ghost-free propagators in nonlocal field theories
• Non-perturbative spectrum of non-local gravity
• High-Energy Scatterings in Infinite-Derivative Field Theory and Ghost-Free Gravity
• Nonperturbative renormalization for the neural network-QFT correspondence
• Radiation from an emitter in the ghost free scalar theory
• Scalar model of effective field theory in curved space
• Weak-field limit and regular solutions in polynomial higher-derivative gravities
• Analysis of a regular black hole in Verlinde's gravity
• Nonlocal generalization of Galilean theories and gravity
• Impulsive waves in ghost free infinite derivative gravity in anti-de Sitter spacetime
• Unitarity and microscopic acausality in a nonlocal theory
• Nonlocality amplifies echoes
• Conformal Symmetry in Field Theory and in Quantum Gravity
• Generalised Boundary Terms for Higher Derivative Theories of Gravity
• Instability of nonsingular black holes in nonlinear electrodynamics
• Quantum radiation from a sandwich black hole
• Form Factors in Quantum Gravity - contrasting non-local, ghost-free gravity and Asymptotic Safety
• Implications of a Simpson-Visser solution in Verlinde's framework
• Asymptotic magnetically charged non-singular black hole and its thermodynamics
• Initial value problem in string-inspired nonlocal field theory
• Towards resolution of anisotropic cosmological singularity in infinite derivative gravity
• Lee-Wick Black Holes
• Confinement and Renormalization Group Equations in String-inspired Non-local Gauge Theories
• Unruh Effect in non local field theories
• Generalized non-local $R^2$-like inflation
• On the contour prescriptions in string-inspired nonlocal field theories
• UV completion of the Starobinsky model, tensor-to-scalar ratio, and constraints on non-locality
• Mass Gap in Infinite Derivative Non-local Higgs: Dyson-Schwinger Approach
• Perturbations in higher derivative gravity beyond maximally symmetric spacetimes
• Renormalization Group in Six-derivative Quantum Gravity
• Higgs Mechanism in Nonlocal Field Theories
• Nonlocal N=1 Supersymmetry
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Strongly Coupled String-inspired Infinite Derivative Non-local Yang-Mills: Diluted Mass Gap
• Recent Progress in Fighting Ghosts in Quantum Gravity
• Palatini formulation of non-local gravity
• Hawking radiation in Non local field theories
• Universality of the Unruh effect
• Quintessence Dark Energy from strongly-coupled Higgs mass gap: Local and Non-local higher-derivative non-perturbative scenarios
• Tests of Quantum Gravity-Induced Non-Locality: Hamiltonian formulation of a non-local harmonic oscillator
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity
• Non-local Starobinsky inflation in the light of future CMB
• Nonsingular black holes and spherically symmetric objects in nonlinear electrodynamics with a scalar field
• Reflection positivity in nonlocal gravity
• Lorentz violation naturalness revisited
• Euclidean scalar field theory in the bi-local approximation
• Quantum solitonic wave-packet of a meso-scopic system in singularity free gravity
• Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifolds
• Cosmology in nonlocal gravity
• Quantum spreading of a self-gravitating wave-packet in singularity free gravity
• New massless and massive infinite derivative gravity in three dimensions
• Stability and causality of multi-local theories
• Bound states of massive complex ghosts in superrenormalizable quantum gravity theories\
• Effective approach to the Antoniadis-Mottola model: quantum decoupling of the higher derivative terms
• Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings
• Gauge invariant renormalizability of quantum gravity
• Extra Dimensions and Fuzzy Branes in String-inspired Nonlocal Field Theory
• Towards UV Finiteness of Infinite Derivative Theories of Gravity and Field Theories
• The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity
• Wavelet field decomposition and UV `opaqueness'
• Fate of the false vacuum in string-inspired nonlocal field theory
• Non-local cosmological models
• New regular 2+1 black hole solutions from bilocal gravity
• Topological defects in nonlocal field theories
• Implications of a matter-antimatter mass asymmetry in Penning-trap experiments
• Renormalization of the bilocal sine-Gordon model
• Gravitational field of scalar lumps in higher-derivative gravity
• Time-periodic solutions of Hamiltonian PDEs using pseudoholomorphic curves
• Conformal invariance versus Weyl invariance
• Fractional Particle and Sigma Model
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Slavnov Identities for Infinite Derivative Theory of Gravity
• Nonlocal Lagrangian fields and the second Noether theorem. Non-commutative $U(1)$ gauge theory
• Kerr-Schild perturbations in higher derivative gravity theories in $D$ dimensions
• Towards Hamiltonian Formalism for String Field Theory and Nonlocality
• Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance
• UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
• Unitarity in Infinite Derivative Theories
• New effective theories of gravitation and their phenomenological consequences
• Conditions for positivity of energy in superrenormalizable polynomial gravity