A canonical dilation of the Schrödinger equation

Autor: M. F. Brown
Rok vydání: 2014
Předmět:
Zdroj: Russian Journal of Mathematical Physics. 21:316-325
ISSN: 1555-6638
1061-9208
Popis: In this paper we shall re-visit the well-known Schrodinger 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 Schrodinger equation, may be obtained as the expectation of a counting process of object-clock interactions.
Databáze: OpenAIRE
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