Covariance of a Physical Theory  

In General > s.a. coordinates; Event; Hole Argument; reference frame; regularization; Relativity Principle.
* Idea: A physical theory is said to be covariant with respect to a certain class of transformations if its basic equations retain their form under those transformations; If the transformations are changes of reference frame, then covariance amounts to the theory satifying the principle of relativity with respect to those transformations; The main examples are Lorentz covariance and general covariance.
* Origin: The term comes from the covariance (and contravariance) of tensors.
@ References: Frewer a1611 [and objectivity].

General Covariance
* Idea: A theory is generally covariant iff it is (a) Invariant under all changes of coordinate system, which is similar to saying that it is diffeomorphism-invariant, or (b) Expressed in terms of only the spacetime metric and other dynamical fields, with no background geometry; To implement it, one usually requires that all fundamental theories be expressed in terms of spacetime tensors, or other objects with well-defined transformation properties under spacetime coordinate trasnformations.
* Remark: This is not always the same as saying that no preferred observer is selected (e.g., such a selection may be possible for cobordisms).
* Remark: Any theory can be reformulated (by putting enough structure among the "variables") so as to satisfy the definition.
@ Background independence: Gryb CQG(10)-a1003 [definition]; Belot GRG(11)-a1106 [explication]; Bärenz a1207; Anderson a1310; Vassallo a1410-in [5D]; Pooley a1506, Cartwright & Flournoy a1512 [vs diffeomorphism invariance]; Anderson a1907 [higher Lie theory and problem of time]; Anderson a1911 [theory].
@ Related topics: 't Hooft pr(89) [2D, discrete model]; Mack gq/97; Bing gq/98 [??]; Francis gq/02 [quantum proposal]; Lusanna & Pauri gq/03 [and gauge]; Mekhitarian & Mkrtchian mp/04 [applications]; Colosi et al CQG(05)gq/04 [model, info and evolution]; Treder & von Borzeszkowski FP(06) [and spacetime structure]; Klajn & Smolić EJP(13) [invariance, covariance and observer independence]; Fatibene et al AP(17)-a1605 [freedom in defining physical states].
> Online resources: see Wikipedia page.

In Different Theories > s.a. reference frames [with quantum reference frames]; relativistic quantum mechanics.
@ In general relativity: Norton FP(89) [Einstein's view and modern view]; Ellis and Matravers GRG(95) [questioning]; Zalaletdinov et al GRG(96); Guo et al PRD(03) [and Noether charges]; Wu & Ruan ht/03 [and general relativity, ??]; Earman in(07) [implications for the ontology and ideology of spacetime]; Lusanna JPCS(06)gq/05 [rev]; Dieks SHPMP(06) [vs equivalence of reference frames]; Giulini LNP(07)gq/06 [issues + historical]; Mashkevich gq/06 ["geometricity"]; Gao & Zhang PRD(07)gq, Sotiriou & Liberati PRD(07)gq [relationship with gravitational dynamics]; Pitts a0911 [artificial gauge freedom and Kretschmann objection]; Chamorro IJTP(13)-a1106; Pitts SHPMP(12)-a1111 [and Ogievetsky-Polubarinov spinors]; Herrera IJMPD(11)-a1111 [and the relevance of observers]; Khoury et al CQG(14)-a1305 [as an accidental or emergent symmetry]; Deser GRG(19) [covariantizing matter fields].
@ Classical field theory: Castrillón-López & Gotay a1008 [covariantizing theories]; Pitts SHPMP(12) [and spinors]; > s.a. types of field theories.
@ Quantum field theory: Brunetti et al CMP(03)mp/01 [algebraic], mp/05 [rev]; Noldus a1102 [and causality]; Fredenhagen & Rejzner a1102-proc [and background independence]; Fewster a1105-proc [vs dynamical locality]; Verch a1105-proc [renormalization ambiguity, and local thermal equilibrium in cosmology]; > s.a. types of quantum field theories [diffeomorphism-invariant].
@ Quantum gravity: Padmanabhan MPLA(88); Kazakov CQG(02); Christodoulakis & Papadopoulos gq/04 [and observables]; Bärenz a1207; Bojowald & Brahma PRD(15)-a1507 [obstacles in lqg, example of Gowdy systems]; Finn et al PRD(20)-a1910 [frame covariance and curved field space]; Chishtie a2102 [loss of general covariance].

Generalizations and Violations
@ Generalied forms: Dąbrowski et al PRD(10)-a0912 [k-deformed covariance].
@ Violations of general covariance: Pirogov gq/06-conf [and extra particles]; Anber et al PRD(10)-a0911 [phenomenology].

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