Precanonical quantization of Yang-Mills fields and the functional Schroedinger representation

TL;DR

This paper explores a covariant precanonical quantization approach to Yang-Mills fields using the De Donder-Weyl formalism, linking it to the functional Schrödinger representation and addressing the mass gap problem through a spectral analysis.

Contribution

It introduces a covariant precanonical quantization framework for Yang-Mills fields and connects it to the functional Schrödinger representation, providing new insights into the mass gap problem.

Findings

Relates the YM mass gap to a spectral problem of a Clifford-valued operator.

Establishes a connection between precanonical quantization and the functional Schrödinger picture.

Proposes a finite-dimensional approach to analyze gauge field quantization.

Abstract

Precanonical quantization of pure Yang-Mills fields, which is based on the covariant De Donder-Weyl (DW) Hamiltonian formalism, and its connection with the functional Schrodinger representation in the temporal gauge are discussed. The YM mass gap problem is related to a finite dimensional spectral problem for a generalized Clifford-valued magnetic Schr\"odinger operator in the space of gauge potentials which represents the DW Hamiltonian operator.