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].
@ 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-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].
@ 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].

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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