Friday, April 5, 2013

1112.5801 (I. V. Kanatchikov)

Precanonical Quantization and the Schrödinger Wave Functional

I. V. Kanatchikov
We address the long-standing issue of the relation between the Schr\"odinger functional representation in quantum field theory and the approach of precanonical field quantization which requires neither a distinguished time variable nor infinite-dimensional spaces of field configurations. The functional Schr\"odinger equation is derived in the limiting case \varkappa \rightarrow \delta(0) from the Dirac-like covariant generalization of the Schr\"odinger equation within the precanonical quantization approach, where the constant \varkappa of the dimension of the inverse spatial volume naturally appears on dimensional grounds. An explicit expression of the Schr\"odinger wave functional as a continuous product of precanonical wave functions on the finite-dimensional covariant configuration space of the field and space-time variables is obtained.
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