Speaker
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.
