• Corpus ID: 119020283

THE STOCHASTIC REPRESENTATION OF HAMILTONIAN DYNAMICS AND THE QUANTIZATION OF TIME

@article{Brown2011THESR,
  title={THE STOCHASTIC REPRESENTATION OF HAMILTONIAN DYNAMICS AND THE QUANTIZATION OF TIME},
  author={Matthew F. Brown},
  journal={arXiv: Mathematical Physics},
  year={2011}
}

• Matthew F. Brown
• Published 30 November 2011
• Mathematics
• arXiv: Mathematical Physics

Here it is shown that the unitary dynamics of a quantum object may be obtained as the expectation of a counting process of object-clock inter- actions. Such a stochastic process arises from the quantization of the clock, and this is derived naturally from the matrix-algebra representation (3) of the nilpo- tent Newton-Leibniz time differential dt. Following (5) we also show that the object-clock interaction dynamics is unitarily equivalent to a pseudo-selfadjoint Schrodinger past-future boundary value problem.