Causality
in Quantum Field Theory |

**In General** > s.a. causality [as emergent]; causality in quantum mechanics; quantum locality and measurement; path
integrals.

* __Idea__:
The vanishing of retarded Green functions outside the lightcone; Theorems (notably
by Hegerfeldt) show that localized particle states violate causality;
Microcausality
is the condition that local observables at spacelike-related points commute (or anticommute); Studying causality in a canonical approach is challenging, given the timeless nature of the formalism; > s.a. quantum locality.

@ __General references__: Shirokov SPU(78);
Maiani & Testa PLB(95);
Hannibal PLB(96);
Keyl CMP(98)
[and observable algebras]; Schroer JPA(99)ht/98, qp/99-proc;
Tommasini qp/01; Tommasini JHEP(02)ht [and
the statistical interpretation of quantum field theory];
Rédei & Summers FP(02), IJTP(07)qp/03-proc;
Greenberg PRD(06)
[microcausality from covariance]; Dubovsky et al PRD(08)-a0709 [vs
Lorentz invariance]; Grinstein et al PRD(09)-a0805 [as
emergent at macroscopic scales]; Finster & Schiefeneder ARMA(13)-a1012 [causal variational principles]; Plimak & Stenholm PRD(11)-a1104, a1104; Plimak et al PS(12)-a1104 [and operator ordering]; Danilkin et al PLB(11) [and unitarity and perturbative expansions]; Benincasa et al CQG(14)-a1206 [superluminal signalling from an ideal measurement of a one-particle wave-packet state]; Healey HSPMP(14)-a1405; Bashkirov a1601 [quantum field theories only know about the causal structure of spacetime].

@ __Related topics__: Kostelecký & Lehnert PRD(01)ht/00 [with
Lorentz and CPT violation]; Plimak & Stenholm AP(08)
[non-linear quantum-statistical
response of the field]; Plimak & Stenholm AP(09) [causality of *R*-normal products of arbitrary field operators]; Eckstein & Miller a1510 [for non-local phenomena].

> __Related topics__: see algebraic
quantum
field theory; energy conditions; perturbative quantum
field theory [causal
perturbation theory]; phase-space approach.

**Specific Types of Theories** > s.a. non-commutative
.

* __ Quantum gravity__: 2015, Elusive–the importance of causality has been stressed for some time, but it is not supported in many approaches, and it is generally expected that microcausality will emerge in some semiclassical limit of the theory, unless some form of causality is built in from the beginning.

@ __Relativistic quantum mechanics__: Butterfield BJPS(07)
[stochastic Einstein locality], ISPS(07)-a0708.

@ __QED__: Kidambi & Widom PLA(99)qp/98,
Widom et al qp/98-conf
[QED]; Plimak & Stenholm a1104 [in the response representation].

@ __Quantum gravity__: Kent in(09)gq/05 [proposed
test]; Fellman et al a0710-conf
[arrow of time and boundary conditions in the early universe]; Marolf PRD(09)-a0808 [consequences
of nature of Hamiltonian]; in Gyongyosi a1403 [causality-cancellation property]; > s.a. geometry in quantum gravity; general relativity; spin-foam
models.

@ __Other types__: Soloviev TMP(05)mp/06,
Joglekar ht/06-conf
[non-local
quantum field theory].

**Causality Violations in Quantum Field Theory** > s.a. quantum field theory in curved backgrounds; violations of lorentz symmetry.

* __Motivation__: QED
vacua, for example, become dispersive media under the influence of external
conditions (background fields, curvature, non-trivial boundary conditions,
finite temperature), and may produce superluminal effects.twt

* __Modeling__: Microcausality
violations can be modeled by fields which do not commute at spacelike-related
points, non-commutative field theory.

* __D-CTC condition__: A condition on states of a quantum communication network, originally proposed by David Deutsch, corresponding to the existence os "backward time-steps" in some of their branches; It may be considered an analogue for quantum processes of the presence of closed timelike curves.

* __2001__: In curved
spacetime, whether there can actually be causality violation (*v*_{front} > *c*)
remains an open question.

@ __Superluminal photon in curved spacetime__: Khriplovich PLB(95);
Daniels & Shore PLB(96);
Dolgov & Novikov PLB(98)gq;
Konstantinov gq/98;
Shore gq/03-proc, CP(03)gq;
Hollowood & Shore PLB(07)-a0707, NPB(08)-a0707 [QED];
Akhoury & Dolgov a1003 [higher-order
perturbation theory], comment Hollowood & Shore a1006 [propagation is dispersive
and causal]; > s.a. modified
QED.

@ __In modified gravity__: Camanho et al a1407, D'Appollonio et al a1502 [with higher-derivative corrections].

@ __Related topics__: Hawking PRD(95)gq [loss
of quantum coherence]; Jain & Joglekar IJMPA(04)ht/03 [non-local *φ*^{4} theory];
Nielsen & Ninomiya IJMPA(09)-a0802 [at
the LHC]; Dubovsky & Sibiryakov JHEP(08)-a0806 [in
2D quantum field theory with broken parity]; Kobakhidze a0811 [and
cmb anisotropy]; Tolksdorf & Verch a1609-CMP [D-CTC condition in quantum field theory].

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