• DOI:10.1134/S1061920814030030
• Corpus ID: 255317240

A canonical dilation of the Schrödinger equation

@article{Brown2014ACD,
  title={A canonical dilation of the Schr{\"o}dinger equation},
  author={M. F. Brown},
  journal={Russian Journal of Mathematical Physics},
  year={2014},
  volume={21},
  pages={316 - 325}
}

• M. F. Brown
• Published 1 July 2014
• Mathematics, Physics
• Russian Journal of Mathematical Physics

In this paper we shall re-visit the well-known Schrödinger equation of quantum mechanics. However, this shall be realized as a marginal dynamics of a more general, underlying stochastic counting process in a complex Minkowski space. One of the interesting things about this formalism is that its derivation has very deep roots in a new understanding of the differential calculus of time. This Minkowski-Hilbert representation of quantum dynamics is called the Belavkin formalism; a beautiful, but not well understood theory of mathematical physics that understands that both deterministic and stochastic dynamics may be formally represented by a counting process in a second-quantized Minkowski space. The Minkowski space arises as a canonical quantization of the clock, and this is derived naturally from the matrix-algebra representation [1, 2] of the Newton-Leibniz differential time increment, dt. And so the unitary dynamics of a quantum object, described by the Schrödinger equation, may be obtained as the expectation of a counting process of object-clock interactions.