Covariant Canonical Quantization
Abstract
A formulation of Covariant Canonical Quantization is discussed, which works on an extended Hilbert space and reduces to conventional canonical quantization when constraining to the solution of the field equation a priori. From the formal point of view it may be seen as a formalism between the canonical operator and the functional integral approach. A covariant number operator and two symmetric vacua are constructed. By that means, certain well-known quantities like the LSZ formula are rederived via a projection limit. The time-ordering operator can be replaced by taking into account the mirrored vacuum as well. Then the quantum field theoretical divergences like the vacuum energy arise a posteriori when a spacetime split is performed. The role of the vacuum energy in different contexts is then discussed in general.
Cite
@article{arxiv.1907.00645,
title = {Covariant Canonical Quantization},
author = {P. Liebrich},
journal= {arXiv preprint arXiv:1907.00645},
year = {2021}
}