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arXiv · 1805.05279

Schr\"odinger wave functional in quantum Yang-Mills theory from precanonical quantization

Igor V. Kanatchikov
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Abstract

A relation between the precanonical quantization of pure Yang-Mills fields and the functional Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger equation together with the quantum Gau\ss\ constraint are derived from the Dirac-like precanonical Schr\"odinger equation.

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Igor V. Kanatchikov. 2018-05-14. Schr\"odinger wave functional in quantum Yang-Mills theory from precanonical quantization. https://doi.org/10.1016/s0034-4877(19)30008-4

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