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December 2014 Precanonical quantization and the Schrödinger wave functional revisited
Igor V. Kanatchikov
Adv. Theor. Math. Phys. 18(6): 1249-1265 (December 2014).


We address the issue of the relation between the canonical functional Schrödinger representation in quantum field theory and the approach of precanonical field quantization proposed by the author, which requires neither a distinguished time variable nor infinite-dimensional spaces of field configurations. We argue that the standard functional derivative Schrödinger equation can be derived from the precanonical Dirac-like covariant generalization of the Schrödinger equation under the formal limiting transition $\gamma^0 \varkappa \to \delta(0)$, where the constant $\varkappa$ naturally appears within precanonical quantization as the inverse of a small “elementary volume” of space. We obtain a formal explicit expression of the Schrödinger wave functional as a continuous product of the Dirac algebra valued precanonical wave functions, which are defined on the finite-dimensional covariant configuration space of the field variables and space-time variables.


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Igor V. Kanatchikov. "Precanonical quantization and the Schrödinger wave functional revisited." Adv. Theor. Math. Phys. 18 (6) 1249 - 1265, December 2014.


Published: December 2014
First available in Project Euclid: 4 December 2014

zbMATH: 1307.81062
MathSciNet: MR3285608

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 6 • December 2014
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