On the precanonical structure of the Schrödinger wave functional
Abstract
We show that the Schrödinger wave functional may be obtained as the product integral of precanonical wave functions on the space of field and spacetime variables. The functional derivative Schrödinger equation underlying the canonical field quantization is derived from the partial derivative covariant analogue of the Schrödinger equation, which appears in the precanonical field quantization based on the De DonderWeyl generalization of the Hamiltonian formalism for field theory. The representations of precanonical quantum operators typically contain an ultraviolet parameter $\varkappa$ of the dimension of the inverse spatial volume. The transition from the precanonical description of quantum fields in terms of Cliffordvalued wave functions and partial derivative operators to the standard functional Schrödinger representation obtained from canonical quantization is accomplished if $\frac{1}{\varkappa}\rightarrow 0$ and $\frac{1}{\varkappa}\gamma_0$ is mapped to the infinitesimal spatial volume element $\mathrm{d}\mathbf{x}$. Thus the standard QFT obtained via canonical quantization corresponds to the quantum theory of fields derived via precanonical quantization in the limiting case of an infinitesimal value of the parameter $\frac{1}{\varkappa}$.
 Publication:

arXiv eprints
 Pub Date:
 December 2013
 DOI:
 10.48550/arXiv.1312.4518
 arXiv:
 arXiv:1312.4518
 Bibcode:
 2013arXiv1312.4518K
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 19 pages. v2: a misprint in Arxiv abstract is corrected. v3: slightly improved linguistically, accepted by ATMP