Non-Local Field Theories  

In General > s.a. locality in quantum field theory.
* Examples: The fractional Klein-Gordon field or modified gravity inspired by quantum loop corrections.
@ General references: Bergman et al PRD(02)ht/01 [and gravity duals]; Gomis et al NPB(04) [physical degrees of freedom]; Soloviev TMP(06) [and non-commutative, axiomatic]; Chicone & Mashhoon AdP(07)-a0708 [from accelerated frames].
@ Phenomenology: Belenchia et al PRD(16)-a1605 [low-energy signatures]; > s.a. higgs mechanism.
@ Special aspects: Calcagni et al PLB(08)-a0712 [localization]; Barnaby NPB(11)-a1005 [initial-value problem]; Addazi IJMPA(16)-a1505 [classicalization as a cure for acausal divergences]; Kegeles & Oriti JPA-a1506 [generalized conservation laws]; Tomboulis PRD(15)-a1507 [initial-value problem, loss of uniqueness]; Belenchia et al PRD(17)-a1707 [exponential suppression of signaling by the non-locality scale]; Saravani CQG(18)-a1801 [path-integral formulation, and dual formulation in terms of local fields]; Basa et al a1907 [classification, area versus volume entanglement]; Buoninfante et al a2001 [theories with ghost-free propagators].
> Special aspects: see causality [action at a distance]; hamiltonian systems; noether theorem.

Specific Types of Theories > s.a. higher-order gravity theories [infinite-order]; higher-order lagrangians.
@ Gauge theories: Capri et al AP(08) [and renormalizability]; Modesto et al PRD(16)-a1506 [Yang-Mills and QED]; > s.a. formulations of electromagnetic theory.
@ Bi-local theories: Naka et al PTP(05)ht/04 [q-deformed]; Diaz et al a1609, Diaz et al IJMPD(18)-a1705 [bilocal scalar field model, and gravity].
@ Other theories: Calcagni & Modesto JPA(14) [string theory].
> Other theories: see fermions; modified quantum field theories; scalar fields; special relativity [non-local]; stochastic quantum mechanics.

Non-Local Gravity > s.a. emergent gravity; massive gravity; Metric-Affine Gravity; types of higher-order theories.
* Motivation: Obtain theories with improved UV behavior with respect to general relativity; Simulate dark matter or dark energy in cosmology.
* Mashhoon's non-local gravity: A generalization of Einstein's theory of gravitation in which non-locality is due to the gravitational memory of past events; It is a dissipative theory, although the damping time scale for gravitational waves of current observational interest is estimated to be at least of the order of the age of the universe; The non-local character of gravity simulates dark matter.
@ General references: Barvinsky PLB(03)ht; Barvinsky PRD(05)ht [action, and strong coupling]; Koshelev a1112-proc; Biswas et al a1302-proc [flat space propagator]; Foffa et al PLB(14)-a1311 [apparent ghost-like instabilities do not describe actual propagating degrees of freedom]; Conroy et al PRD(15)-a1509 [D dimensions, graviton propagator, entropy, bouncing cosmology]; Briscese & Pucheu IJGMP(16)-a1511 [Palatini formulation]; Maggiore PRD(16)-a1603 [the non-locality cannot emerge from perturbative quantum loop corrections due to light particles]; Maggiore a1606 [rev]; Belgacem et al JCAP(18)-a1712 [conceptual aspects and cosmology]; Calcagni et al JHEP(18)-a1803 [initial conditions and degrees of freedom]; Woodard a1807-proc [arguments]; Calcagni Univ(18)-a1809 [diffusion method to solve the non-linear field equations]; Boos a2009-PhD [including didactic introduction]; Modesto a2103 [withn matter].
@ Hamiltonian formalism: Klusoň JHEP(11)-a1105; Joshi et al a1909.
@ Mashhoon proposal: Mashhoon AdP(07)ht/06; Blome et al PRD(10)-a1002 [Newtonian regime]; Mashhoon in(11)-a1101; Chicone & Mashhoon JMP(12)-a1111 [modified Poisson equation]; Mashhoon CQG(13)-a1304 [damping of gravitational waves]; Mashhoon PRD(14)-a1409 [non-local generalization of Einstein's equation, and linear approximation]; Mashhoon Gal-a1411 [rev]; Bini & Mashhoon IJGMP(16)-a1605 [conformally flat spacetimes]; Puetzfeld et al PRD(19)-a1903; Mashhoon & Hehl Univ(19)-a1908 [gravitomagnetism].
@ Other types of theories: Calcagni & Nardelli PRD(10)-a1004 [inspired by the effective action of p-adic string and string field theory]; Biswas et al PRL(12)-a1110 [ghost-free theories]; Barvinsky PRD(12)-a1112; Dimitrijevic et al PIM-a1411; Dragovich SPMS(14)-a1508; Giaccari & Modesto a1605 [supersymmetric extension]; Amendola et al PRD(17)-a1707 [quantum-gravity inspired]; Modesto & Rachwał JPCS(17)-a1801 [conformally invariant theories, and spacetime singularities]; Tian PRD(18)-a1808 [scalar-tensor theory].
@ As effective dark matter: Hehl & Mashhoon PLB(09)-a0812, PRD(09)-a0902; Barvinsky PLB(12)-a1107 [and effective cosmological constant]; Arraut IJMPD(14)-a1310 [and MONDian dark matter]; > s.a. dark-matter types.
@ As effective dark energy: Arkani-Hamed et al ht/02 [cosmological constant]; Foffa et al IJMPA(14)-a1311; Maggiore & Mancarella PRD(14)-a1402; Cusin et al PRD(16)-a1512 [with a Weyl-square term]; > s.a. cosmological-constant problem; cosmological acceleration.
@ Cosmology, stability: Elizalde et al PRD(12)-a1110 [de Sitter spacetime]; Nersisyan et al PRD(17)-a1610 [in tensorial theories]; Briscese et al PRD(19)-a1901; > s.a. minkowski spacetime.
@ Structure formation: Dodelson & Park PRD(14)-a1310 [Deser-Woodard model]; Rahvar & Mashhoon PRD(14)-a1401 [galaxies]; Dirian et al JCAP(14)-a1403 [and cosmological perturbations]; Nersisyan et al JCAP(17)-a1701 [Deser-Woodard model]; Roshan & Rahvar ApJ(19)-a1901 [spiral galaxies].
@ Other cosmology: Soussa & Woodard CQG(03)ap [and MOND]; Hamber & Williams MPLA(06)gq/05; Deser & Woodard PRL(07)-a0706; Nojiri & Odintsov PLB(08)-a0708; Koivisto PRD(08); Tsamis & Woodard JCAP(14)-a1405 [caveat]; Koshelev & Vernov PPN(14)-a1406 [solutions]; Dirian et al JCAP(15)-a1411 [cosmological predictions]; Mitsou a1504-PhD; Zhang et al JCAP(16)-a1511; Chicone & Mashhoon JMP(16)-a1510 [Newtonian cosmology]; Dimitrijevic et a proc(16)-a1701 [some solutions]; Chicone & Mashhoon a1703; > s.a. FLRW models.
@ Quantization: De Felice & Sasaki PLB(15)-a1412 [ghosts]; Talaganis PoS-a1508 [toy model, 1-loop and 2-point functions].
@ Other phenomenology: Kehagias & Maggiore JHEP(14)-a1401 [spherically symmetric static solutions]; Chicone & Mashhoon CQG(16)-a1508 [perihelion precession]; Zhang et al JHEP(16)-a1601 [acausality problem]; Calcagni & Modesto PLB(17)-a1707 [stability of the Schwarzschild singularity]; Calcagni et al PLB(18)-a1803 [black-hole formation and stability]; Giaccari & Modesto a1803 [consistent with causality]; Dialektopoulos et al PRD(19)-a1812 [orbits of stars around Sgr A*]; Belgacem et al JCAP(19)-a1812 [lunar laser ranging]; Nascimento et al a2102 [causality]; > s.a. gravitational radiation; semiclassical gravity.

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