Observers and Observables in Physical Theory  

Observers > s.a. Covariance; reference frames [including accelerated].
* Types of observers: Lagrangian (non surface-forming observers) or Eulerian (surface-forming ones, or hypersurface-orthogonal), inertial or non-inertial.
* Observer space: The 'observer space' of a Lorentzian spacetime is the space of future-timelike unit tangent vectors.
@ Role of observers: Klajn & Smolić EJP(13)-a1302 [comments]; Knuth CP(14)-a1310 [observer-centric physics].
@ Accelerated observers: Mashhoon AdP(13)-a1211 [non-local connection between non-inertial and inertial observers]; Kolekar PRD(14) [in a thermal bath]; > s.a. observables in classical gravity [non-inertial].
@ In general spacetimes: Page CQG(98)gq/97 [stationary axisymmetric, maximal acceleration]; Garat JMP(05)-a1306 [Euler observers in geometrodynamics]; Dahia & Felix da Silva GRG(11)-a1004 [static]; Dupré a1403 [two symmetric tensors observed to be equal by all observers at a specific event are necessarily equal at that event]; Chęcińska & Dragan PRA(15)-a1509 [communication between observers without a shared reference frame].
@ Physics in observer space: Gielen & Wise JMP(13)-a1210 [observer-space formulation of general relativity]; Gielen PRD(13)-a1301 [observer-space geometry].
@ In quantum theory: Konishi IJMPB(12)-a1212 [and time-reparametrization symmetry].

Observables > s.a. information; Observers.
$ Idea: When there are no constraints, an observable for a classical theory is any measurable function on the phase space Γ for a theory; In quantum theory, this leads to operators on the Hilbert space of the theory; Since classical observables are usually real, quantum operators are usually self-adjoint.
* Remark: There are observables for which actually constructing a measuring apparatus is difficult or impossible.
* Linear theory: Linear observables are labelled by vectors XΓ, and given by wX(V) = Ω(X, V), for all VΓ.
* Theory with constraints: In addition, (for Dirac observables) the Poisson brackets with the constraints must weakly vanish.
@ General references: Fernández PLA(03) [perturbative]; de Groote mp/06; Hartmann FP-a1504 [and foundations of physics]; Anderson a1505 [differential equations].
@ Theories with constraints: Lusanna ht/95-conf [presymplectic approach]; Hájíček CQG(96)gq/95 [and time evolution]; Lucenti et al JPA(98) [N relativistic particles]; Dütsch & Fredenhagen CMP(99)ht/98 [gauge theories]; Bratchikov IJGMP(07)ht/04 [space of orbits vs gauge fixing], JGP(06) [second-class]; Hellmann a0812 [kinematic observables, physical interpretation]; Pons et al PRD(09)-a0905 [generally covariant theories and gauge]; Quadri EPJC(10)-a1007 [non-linearly realized gauge theories].

Related Topics > see Coarse-Graining; conservation laws; lattice theories [observable currents].

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