Locality in Quantum Field Theory |

**In General** > s.a. locality; localization;
observables; quantum field theory; quantum
particles and states.

* __Physics in a bounded region__:
It cannot be discussed in terms of subspaces of the full Hilbert space \(\cal H\),
because fields there generate \(\cal H\) when acting on the vacuum (> see
Reeh-Schlieder theorem); One can use local
algebras of operators.

* __Non-local theories__: For example,
a non-local version of QED; Observables in quantum gravity have to be non-local.

> __Types of theories__:
see generalized quantum field theories [non-local];
types of quantum field theories [ultralocal, locally covariant].

**Specific Theories** > s.a. light
[standstill]; non-commutative field theories.

* __Non-locality in quantum
gravity__: It has been suggested by Markopoulou & Smolin that
in a transition from an early quantum geometric phase of the universe
to a low-temperature phase characterized by an emergent spacetime metric,
locality might have been "disordered", with a mismatch between
micro-locality and macro-locality.

@ __Quantum gravity, non-locality__:
Ahluwalia PLB(94);
Prugovečki FP(96)gq;
Giddings PRD(06)ht [and strings],
PRD(06)ht [argument from black hole physics];
Markopoulou & Smolin CQG(07)gq [lqg states];
Sorkin in(08)gq/07 [at scales larger than \(l_{\rm P}\)];
Smrz NCB(06);
Arzano et al MPLA(10)-a0806 [and hidden entanglement, unitarity];
Prescod-Weinstein & Smolin PRD(09)-a0903 [and effective dark energy];
Giddings PRD(13)-a1211 [and quantum black-hole evolution];
Weinstein a1211-FQXi [and correlations];
Dittrich et al CQG(14)-a1404 [and discretization independence];
Barvinsky MPLA(15)-a1408 [and cosmology];
Giddings JHEP(15)-a1503 [and Hilbert space structure, entanglement];
Azimov IJMPA(16)-a1508-proc;
Donnelly & Giddings PRD(16)-a1607
[implications of diffeomorphism invariance, relational approaches];
Maziashvili & Silagadze JPCS-a1812;
> s.a. entanglement; non-commutative geometry;
quantum regge calculus; spacetime foam.

@ __Quantum gravity, recovering locality__: Hardy a0804-in [formalism locality];
Amelino-Camelia et al PRL(11) [taming non-locality by giving up absolute coincidence of events];
Engelhardt & Fischetti IJMPD(17)-a1703 [in holographic theory, all or nothing recovery];
> s.a. approaches to quantum gravity.

@ __QED__: Valentini in(90);
Moussa & Baseia PLA(98) [single particle in cavity QED];
> s.a. photon; QED phenomenology.

@ __Fermions__: Oeckl QSMF(16)-a1307 [free fermions];
> s.a. localization.

@ __Other theories__: Buchholz & Fredenhagen LNP(82) [gauge theory, and particle states];
Chernitskii in(02)qp/03 [and unified theory];
Balachandran et al PRD(08)-a0708 [twisted quantum field theory];
Fewster & Verch AHP(12)-a1109 [scalar field, dynamical locality];
Benini a1503-PhD [Abelian gauge theories];
Calmet et al EPJC(15)-a1505 [non-locality due to general relativity];
Aste & Frensel a1510
[localization properties and causality aspects of massless and massive scalar particles];
> s.a. deformed special relativity.

> __Lattice theories__:
see ising model [with non-local links];
lattice field theory [localization in random lattices].

**References**

@ __General references__:
Muller & Butterfield PhSc(94)sep;
Gottschalk LMP(99)mp/04 [in terms of Wightman functions, in momentum space];
Chernitskii qp/01;
Brunetti et al CMP(03)mp/01 [generally covariant locality];
Bostelmann JMP(05)mp/04;
Wanng JMP(98)qp/05 [non-locality];
Kahn & Thaler JHEP(12)-a1202 [locality in theory space, and dimensional reduction];
Brunetti et al RVMP(14)-a1206 [in algebraic quantum field theory];
Lin AP(12)-a1211 [instantaneous spatially-local measurements in relativistic quantum field theories];
Pavšič a1705.

@ __Physics in a bounded region__: Reeh & Schlieder NC(61);
in Haag 92;
Strohmaier et al JMP(02)mp [in curved spacetime].

@ __Related topics__: Tommasini ht/01,
ht/01 [and correlations];
Rejzner a1906-proc [groups with causality].

> __Online resources__:
Wikipedia page on the Reeh-Schlieder theorem.

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