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*_{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 a1607
[implications of diffeomorphism invariance, relational approaches];
> s.a. 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 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 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].

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

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send feedback and suggestions to bombelli at olemiss.edu – modified 13
aug
2017