Schrödinger wave functional in quantum Yang-Mills theory from precanonical quantization

2018/05/31 by Igor V. Kanatchikov · 2 citations
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP

paper · pdf · doi:10.1016/s0034-4877(19)30008-4

published as Rep. Math. Phys. 82 (2018) 373 · 15 pages. V2: tiny changes in the text, 4 refs added, to appear in Rep. Math. Phys

arxiv created 2018/09/28 · arxiv updated 2019/02/20

Abstract

A relation between the precanonical quantization of pure Yang-Mills fields and the functional Schrödinger representation in the temporal gauge is discussed. It is shown that the latter can be obtained from the former when the ultraviolet parameter \varkappa introduced in precanonical quantization goes to infinity. In this limiting case, the Schrödinger wave functional can be expressed as the trace of the Volterra product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration, and the canonical functional derivative Schrödinger equation together with the quantum Gauß constraint are derived from the Dirac-like precanonical Schrödinger equation.

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