2018/12/29 by I. V. Kanatchikov, Kanatchikov, I. V.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1812.11264
13 pages. arXiv admin note: text overlap with arXiv:1810.09968
arxiv created 2018/12/29 · arxiv updated 2019/02/08
A relationship between the functional Schrödinger representation and the precanonical quantization of a scalar field theory is extended to an arbitrary curved space-time. The canonical functional derivative Schrödinger equation is derived from the manifestly covariant precanonical Schrödinger equation and the Schrödinger wave functional is expressed as the trace of the product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration when the ultraviolet parameter \varkappa introduced in precanonical quantization is infinite. Thus the standard QFT in functional Schrödinger representation emerges from the precanonical formulation of quantum fields as a singular limiting case.