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Bulletin of the American Physical Society

A Second Dimension of Time Explains Quantum and Classical Fields

Richard Kriske

Published Apr 8, 2014• 0 citations
Publisher
DOI
10.1103/baps.2014.april.y9.2

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We show that the time dependence of correlation functions in an extended quantum system in d dimensions, which is prepared in the ground state of some Hamiltonian and then evolves without dissipation according to some other Hamiltonian, may be extracted using methods of boundary critical phenomena in d + 1 dimensions. For d = 1 particularly powerful results are available using conformal field theory. These are checked against those available from solvable models. They may be explained in terms of a picture, valid more generally, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate classically through the system.
If "quantization is an art", it can be greatly refined through the formalism of cyclic time. In past papers, we have demonstrated the effectiveness of a unified formulation of quantum and classical physics based on cyclic relativistic time. In this paper, we show, using theorems from Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics, classical in essence, lead naturally to the canonical commutation relations and the other quantization rules of standard Quantum Mechanics. Our results suggest that canonical quantization can be interpreted as an implicit imposition of closed time paths on classical dynamics, without explicitly stating that time is a cyclic dimension.