Detailed Information on Publication Record

@book{60889,
   author = {Khavkine, Igor},
   keywords = {local observables; differential invariants; QFT in curved spacetime; Pseudo-Riemannian geometry; Constant curvature; Differential complex; Sheaf cohomology; Linearized gravity; cosmology; equivalence up to isometry; IDEAL characterization; Schwarzschild; Tangherlini; warped product; Birkhoff's theorem; linearized gravity; gauge-invariant observables; FLRW},
   language = {eng},
   title = {Invariants in Relativity and Gauge Theory},
   year = {2019}
}

TY  - 
ID  - 60889
AU  - Khavkine, Igor
PY  - 2019
TI  - Invariants in Relativity and Gauge Theory
KW  - local observables
KW  - differential invariants
KW  - QFT in curved spacetime
KW  - Pseudo-Riemannian geometry
KW  - Constant curvature
KW  - Differential complex
KW  - Sheaf cohomology
KW  - Linearized gravity
KW  - cosmology
KW  - equivalence up to isometry
KW  - IDEAL characterization
KW  - Schwarzschild
KW  - Tangherlini
KW  - warped product
KW  - Birkhoff's theorem
KW  - linearized gravity
KW  - gauge-invariant observables
KW  - FLRW
N2  - In mathematical physics, one of the goals in the study of classical  eld theory (essentially, a variational partial di erential equation (PDE)) with gauge symmetries (a.k.a gauge theories) is a precise and rigorous construction of the corresponding reduced phase space [6, 12, 22, 23]: the space of solutions, endowed with the canonical Poisson structure, and quotiented by the gauge transformations. A large number of technical problems stands in the way, including but not limited to describing the solutions of a non-linear PDE as an in nite dimensional space with some kind of smooth structure, specifying a su ciently regular class of functions on this space on which the Poisson structure is well-de ned, explicitly describing the structure of the quotient, or alternatively the structure of the functions invariant under gauge symmetries. The functions in the latter class are referred to as gauge-invariant observables (or invariants). The scope of this Habilitation Thesis is to address some purely geometric problems that arise in the study of gauge-invariant observables and can be attacked using tools from the theory of di erential invariants [30] and the theory of formal integrability of overdetermined PDEs [31, 35]. The main focus is on General Relativity (GR) as a non-trivial representative example, but the perspective is such that the tools used would also apply to other gauge theories, of which Electrodynamics, Yang-Mills, Chern-Simons, Supergravity and many other models used in fundamental theoretical physics and geometry [12], are prominent examples. The papers collected in this Thesis consist of [25], [27], [26], [10], [28], [29], all of which have been published with the exception of [29], which has been submitted for publication to Communications in Mathematical Physics. In the remainder of the Introduction, we give a brief summary of relevant geometric notions(Section 0.1) and summarize the main problems addressed and results obtained in the above papers, grouped by theme in Sections 0.2, 0.3 and 0.4.
ER  - 

KHAVKINE, Igor. \textit{Invariants in Relativity and Gauge Theory}. 2019.