Abstract
Polymomentum canonical theories, which are manifestly covariant multiparameter generalizations of the Hamiltonian formulation to field theory, are considered as a possible basis of quantization. We arrive at a multi-parameter hypercomplex generalization of quantum mechanics to field theory in which complex numbers and a time parameter are replaced by the space-time Clifford algebra and space-time variables appearing on equal footing. The corresponding covariant generalization of the Schrödinger equation fulfills several aspects of the correspondence principle: a relation to the Hamilton-Jacobi equation in the classical limit and the Ehrenfest theorem. A relation of the corresponding wave function (over a finite dimensional configuration space of field and space-time variables) to the Schrödinger wave functional in quantum field theory is examined in the ultra-local approximation.
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
