Spin-2 Fields| Spin-2 Fields |
In General
> s.a. graviton; Pauli-Fierz Theory;
theories of gravity; types of gauge theories.
* Remark: For a linear
theory, consistency requires that a second-order field equation for
a free massless rank-2, symmetric tensor field on some background be
the linearized Einstein equation; On the other hand, non-linear
generalizations of a spin-2 linear field theory can have different
symmetry groups; When the fields are geometrized and the theory made
diffeomorphism-invariant, one gets the non-linear dynamics of general
relativity (or as the torsion of a Cartan geometry), or a higher-order
theory; In other words, the only known fully ghost-free and consistent
Lorentz-invariant kinetic term for a spin-2 field is the Einstein-Hilbert
term (and the field is the graviton).
* Field equations:
Described by a symmetric hab;
In the massless case,
∂c∂c hab + ∂a∂b h − 2 ∂c∂(a hb) c − ηab ∂c∂c h + ηab ∂c∂d hcd = 0 .
@ General references: in Wentzel 49;
van Nieuwenhuizen NPB(73) [and linearized general relativity];
Wald PRD(86) [and general covariance],
CQG(87),
in(88);
Cutler & Wald CQG(87);
Heiderich & Unruh PRD(88);
Friedrich CQG(03) [near infinity];
in Franklin 10 [IIb];
Arcos et al CQG(10)-a1001 [as translation-Lie-algebra-valued vector field];
Arcos et al FP(12)-a1110 [helicity];
Folkerts et al a1107;
Cirilo-Lombardo G&C-a1405 [Bronstein's work on quantization and wave equations];
Naruko et al PRD(19)-a1812 [Lorentz-invariant theories];
Jezierski et al a2004 [localized energy].
@ Interactions: Hinterbichler & Rosen JHEP(12)-a1203 [in arbitrary dimensions, without Boulware-Deser ghosts];
Mayor et al G&C(13) [conformally and gauge-invariant field equations];
Gao PRD(14)-a1403 [Lorentz-invariant derivative interactions];
Noller JCAP(15)-a1409 [consistent kinetic and derivative interactions];
de Rham et al CQG(15)-a1410 [for charged spin-2 fields];
Afshar et al JHEP(15)-a1410 [3D];
Hertzberg & Sandora JHEP(17)-a1702 [and causality].
@ Related topics: Buchbinder et al PLB(99)ht [in string theory];
Boulanger et al ht/00-proc [consistency];
Magnano & Sokołowski AP(03) [and higher-derivative];
Blas JPA(07)ht-in [without ghosts or tachyons];
Buchbinder et al PLB(10)-a0912 [BRST Lagrangian construction];
Ben Achour et al PRD(14)-a1311 [conformally-invariant wave equation, in d dimensions];
Noller et al JCAP(14)-a1311 [interacting, in the Stückelberg picture];
Hertzberg & Sandora PRD(17)-a1704
[theories of massless spin-2 and spin-1 particles, soft gravitons, and special relativity].
In Curved Spacetime
> s.a. asymptotic flatness at null infinity;
fields in schwarzschild spacetime.
@ General references: Bengtsson JMP(95)gq/94;
Novello & Neves CQG(02)gq [Fierz representation];
Deser & Henneaux CQG(07)gq/06 [re consistency];
Papini PRD(07)gq;
Zecca IJTP(09) [in FLRW spacetime];
Grisa & Sorbo PLB(10) [Pauli-Fierz gravitons in FLRW spacetime];
> s.a. schwarzschild
and kerr spacetimes.
@ Using a non-symmetric tensor:
Dalmazi et al PRD(17)-a1706,
Mazuet & Volkov JCAP(18)-a1804 [massive];
Fortes & Dalmazi PRD(19)-a1901 [massless and partially massless].
@ In (A)dS spacetime:
Deser & Waldron PLB(01),
Polishchuk TMP(04) [massive, AdS];
Gabadadze et al a0809 [massive, de Sitter space];
Zinoviev MPLA(09) [massless, electromagnetic interactions];
Zinoviev NPB(09)-a0901 [massive, electromagnetic interactions].
@ Other cosmology: Tamanini et al JCAP(14)-a1307;
Barceló et al PRD(14)-a1401,
AP(18)-a1406 [graviton self-interactions and the cosmological constant];
Maia IJMPA(16)-a1509.
@ Coupled to gravity: Buchbinder et al NPB(00)ht/99 [coupled to gravity];
Hassan et al JHEP(13)-a1208 [massive];
Joung et al PRL(14)-a1406,
García-Saenz et al JHEP(16)-a1511 [partially massless, no-go theorems].
Other Variations > s.a. bimetric theory.
@ General references: López-Pinto gq/04 [non-standard].
@ Massive: Zinoviev JHEP(05)ht [dual formulation],
NPB(07) [possible interactions];
Folkerts et al CEJP-a1310 [and non-linear completion];
Hod CQG(13)-a1402 [late-time tails];
Ohara et al PRD(14)-a1402 [renormalizable theory];
Akagi et al PRD(14)-a1410 [in curved spacetime, with non-minimal coupling, ghost-free];
Nojiri a1411-proc [new ghost-free model];
Bonifacio et al PRD(15)-a1501 [TDiff and Weyl invariant];
Koenigstein et al AP(16)-a1508 [non-interacting, classical and quantum theory];
Ohara PRD(16)-a1606 [charged, self-interacting];
Akagi a1810 [in curved spacetime];
Curtright & Alshal NPB(19)-a1907 [massive dual spin-2 field theory];
Alberte et al JHEP(20)-a1910 [interacting massive spin-2 fields, effective field theory];
Dalmazi & dos Santos a2003 [dual actions].
@ In electromagnetic background:
Klishevich & Zinoviev PAN(98)ht/97 [massive];
Novello et al ht/03
& ht/03,
Deser & Waldron ht/03 [acausality].
@ And torsion: Novello gq/02;
Nair et al PRD(09)-a0811 [massive, from torsion, in curved spacetime];
> s.a. schwarzschild spacetime.
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