Seventeenth Marcel Grossmann Meeting

Quantization without 3+1 decomposition in curved spacetime and its Schroedinger picture limit

8 Jul 2024, 18:20

10m

M4 ( Palazzo Micara of the ‘Gabriele d’Annunzio’ University)

Talk in a parallel session Quantum field theory in curved spacetimes and perturbative quantum gravity

Speaker

Igor Kanatchikov (Natl Quantum Information Center)

Description

We present an approach to field quantization in curved spacetime which is based on the De Donder-Weyl Hamiltonian theory where space and time dimensions are treated on an equal footing. This leads to a description in terms of Clifford algebra valued wave functions on the bundle of field variables an spacetime variables, and a Dirac-like analog of the Schroedinger equation for this universal wave function. The procedure of quantization (of Poisson-Gerstenhaber brackets of differentail forms) requires introduction of an ultraviolet parameter $\varkappa$ on purely dimensional grounds. We analyze a relation of this approach to the standard QFT in curved spacetime and demonstrate that the Schr\"odinger functional representation of the latter is reproduced, after $3+1$ decomposition, in the limit of infinitesimal $1/\varkappa$. In this limit, the Schroedinger wave functional appears as a product integral of precanonical wave functions, both in static and non-static spacetimes.