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 field theory.
* 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]; Gyongyosi QE(20)-a1603; Smolin a1805-in [temporal relationalism]; Donoghue & Menezes PRL(19)-a1908 [arrow of causality]; > 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]; Varadarajan CQG(17) and CQG+ [1+1 polymer scalar field theory, propagation as a property of physical states].

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.
* 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 (vfront > 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 JHEP(16)-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 φ4 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 CMP(18)-a1609 [D-CTC condition in quantum field theory]; Jia a1805-GRF, a1902 [with indefinite causal structure].

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 12 mar 2020