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General relativity and the AKSZ construction. (English) Zbl 1470.81055

In the article under reviewing the authors apply the previous Alexandrov-Kontsevich-Schwarz-Zaboronski ( AKSZ) construction [M. Alexandrov et al., Int. J. Mod. Phys. A 12, No. 7, 1405–1429 (1997; Zbl 1073.81655)] to the Batalin-Fradkin-Vilkovysky description of the reduced phase space both Einstein-Hilbert action and of the Palatini-Cartan theory in every space-time dimension greater than 2. The authors make a comparison between the case of Einstein-Hilbert and Palatini-Cartan cases. One found that in the previous ( PC) case one recover a Batalin-Vilkovysky theory for the first order formulation of an Einstein-Hilbert theory. While in the later case one agree with Batalin-Vilkovysky theory for Palatini-Cartan theory with partial implementation of the torsion-free condition. All the theories investigated here are Batalin-Vilkovysky versions of the same classical system on cilinders. The study given here have the advantage of giving a compatible BV-Batalin-Fradkin-Vilkovysky description which represents a necessary starting point for quantization in a presence of a boundary.

MSC:

81T70 Quantization in field theory; cohomological methods
81V17 Gravitational interaction in quantum theory
83C47 Methods of quantum field theory in general relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
58C50 Analysis on supermanifolds or graded manifolds
58D25 Equations in function spaces; evolution equations
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
53Z05 Applications of differential geometry to physics

Citations:

Zbl 1073.81655
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