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Schrödinger wave functional in quantum Yang-Mills theory from precanonical quantization. (English) Zbl 1441.81129
Summary: A relation between the precanonical quantization of pure Yang-Mills fields and the standard functional Schrödinger representation in the temporal gauge is established. 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 field configuration, and the canonical functional derivative Schrödinger equation together with the quantum Gauss constraint is derived from the Dirac-like precanonical Schrödinger equation.
##### MSC:
 81T70 Quantization in field theory; cohomological methods 35J10 Schrödinger operator, Schrödinger equation 81T13 Yang-Mills and other gauge theories in quantum field theory 81S08 Canonical quantization
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